- -

On realcompact topological vector spaces

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

On realcompact topological vector spaces

Show simple item record

Files in this item

dc.contributor.author Kakol, Jerzy Marian es_ES
dc.contributor.author López Pellicer, Manuel es_ES
dc.date.accessioned 2016-12-21T09:14:16Z
dc.date.available 2016-12-21T09:14:16Z
dc.date.issued 2011
dc.identifier.issn 1578-7303
dc.identifier.uri http://hdl.handle.net/10251/75518
dc.description.abstract [EN] This survey paper collects some of older and quite new concepts and results from descriptive set topology applied to study certain infinite-dimensional topological vector spaces appearing in Functional Analysis, including Frechet spaces, (L F)-spaces, and their duals, (D F)-spaces and spaces of continuous real-valued functions C(X) on a completely regular Hausdorff space X. Especially (L F)-spaces and their duals arise in many fields of Functional Analysis and its applications, for example in Distributions Theory, Differential Equations and Complex Analysis. The concept of a realcompact topological space, although originally introduced and studied in General Topology, has been also studied because of very concrete applications in Linear Functional Analysis. es_ES
dc.description.sponsorship The research for the first named author was (partially) supported by Ministry of Science and Higher Education, Poland, Grant no. NN201 2740 33 and for the both authors by the project MTM2008-01502 of the Spanish Ministry of Science and Innovation.
dc.language Inglés es_ES
dc.publisher Springer es_ES
dc.relation MNiSW/NN201 2740 33
dc.relation info:eu-repo/grantAgreement/MICINN//MTM2008-01502/ES/ELEMENTOS DE TOPOLOGIA DESCRIPTIVA DE CONJUNTOS EN ANALISIS FUNCIONAL LINEAL/
dc.relation.ispartof Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas es_ES
dc.rights Reconocimiento - No comercial (by-nc) es_ES
dc.subject Angelicity es_ES
dc.subject Baire and (b-) Baire-like es_ES
dc.subject Bornological es_ES
dc.subject Borel set es_ES
dc.subject C*-embedded es_ES
dc.subject Class B es_ES
dc.subject (DF) space es_ES
dc.subject Distinguished space es_ES
dc.subject Frechet-Urysohn es_ES
dc.subject k-Space es_ES
dc.subject K-Analytic es_ES
dc.subject (Weakly) Lindelof (Sigma) es_ES
dc.subject Locally convex space es_ES
dc.subject (Sigma-)Quasi-Suslin space es_ES
dc.subject (Strongly) realcompact space es_ES
dc.subject Talagrand compact es_ES
dc.subject (Countable) tightness es_ES
dc.subject Trans-separable es_ES
dc.subject Weakly compact es_ES
dc.subject (WCG) space es_ES
dc.subject Web-bounded (compact) es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On realcompact topological vector spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s13398-011-0003-0
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural es_ES
dc.description.bibliographicCitation Kakol, JM.; López Pellicer, M. (2011). On realcompact topological vector spaces. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 105(1):39-70. https://doi.org/10.1007/s13398-011-0003-0 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://dx.doi.org/10.1007/s13398-011-0003-0 es_ES
dc.description.upvformatpinicio 39 es_ES
dc.description.upvformatpfin 70 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 105 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 41382 es_ES
dc.identifier.eissn 1579-1505
dc.contributor.funder Ministerio de Ciencia e Innovación
dc.contributor.funder Ministry of Science and Higher Education, Polonia
dc.relation.references Argyros S., Mercourakis S.: On weakly Lindelöf Banach spaces. Rocky Mountain J. Math. 23(2), 395–446 (1993). doi: 10.1216/rmjm/1181072569 es_ES
dc.relation.references Arkhangel’skii, A. V.: Topological Function Spaces, Mathematics and its Applications, vol. 78, Kluwer, Dordrecht (1992) es_ES
dc.relation.references Batt J., Hiermeyer W.: On compactness in L p (μ, X) in the weak topology and in the topology σ(L p (μ, X), L p (μ,X′)). Math. Z. 182, 409–423 (1983) es_ES
dc.relation.references Baumgartner J.E., van Douwen E.K.: Strong realcompactness and weakly measurable cardinals. Topol. Appl. 35, 239–251 (1990). doi: 10.1016/0166-8641(90)90109-F es_ES
dc.relation.references Bierstedt K.D., Bonet J.: Stefan Heinrich’s density condition for Fréchet spaces and the characterization of the distinguished Köthe echelon spaces. Math. Nachr. 35, 149–180 (1988) es_ES
dc.relation.references Cascales B.: On K-analytic locally convex spaces. Arch. Math. 49, 232–244 (1987) es_ES
dc.relation.references Cascales B., Ka̧kol J., Saxon S.A.: Weight of precompact subsets and tightness. J. Math. Anal. Appl. 269, 500–518 (2002). doi: 10.1016/S0022-247X(02)00032-X es_ES
dc.relation.references Cascales B., Ka̧kol J., Saxon S.A.: Metrizability vs. Fréchet–Urysohn property. Proc. Am. Math. Soc. 131, 3623–3631 (2003) es_ES
dc.relation.references Cascales B., Namioka I., Orihuela J.: The Lindelöf property in Banach spaces. Stud. Math. 154, 165–192 (2003). doi: 10.4064/sm154-2-4 es_ES
dc.relation.references Cascales B., Oncina L.: Compactoid filters and USCO maps. J. Math. Anal. Appl. 282, 826–843 (2003). doi: 10.1016/S0022-247X(03)00280-4 es_ES
dc.relation.references Cascales B., Orihuela J.: On compactness in locally convex spaces, Math. Z. 195(3), 365–381 (1987). doi: 10.1007/BF01161762 es_ES
dc.relation.references Cascales B., Orihuela J.: On pointwise and weak compactness in spaces of continuous functions. Bull. Soc. Math. Belg. Ser. B 40(2), 331–352 (1988) Journal continued as Bull. Belg. Math. Soc. Simon Stevin es_ES
dc.relation.references Diestel J.: $${L^{1}_{X}}$$ is weakly compactly generated if X is. Proc. Am. Math. Soc. 48(2), 508–510 (1975). doi: 10.2307/2040292 es_ES
dc.relation.references van Douwen E.K.: Prime mappings, number of factors and binary operations. Dissertationes Math. (Rozprawy Mat.) 199, 35 (1981) es_ES
dc.relation.references Drewnowski L.: Resolutions of topological linear spaces and continuity of linear maps. J. Math. Anal. Appl. 335(2), 1177–1195 (2007). doi: 10.1016/j.jmaa.2007.02.032 es_ES
dc.relation.references Engelking R.: General Topology. Heldermann Verlag, Lemgo (1989) es_ES
dc.relation.references Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, J., Zizler, V.: Functional Analysis and Infinite-Dimensional Geometry. Canadian Mathematical Society. Springer, Berlin (2001) es_ES
dc.relation.references Ferrando J.C.: A weakly analytic space which is not K-analytic. Bull. Aust. Math. Soc. 79(1), 31–35 (2009). doi: 10.1017/S0004972708000968 es_ES
dc.relation.references Ferrando J.C.: Some characterization for υ X to be Lindelöf Σ or K-analytic in term of C p (X). Topol. Appl. 156(4), 823–830 (2009). doi: 10.1016/j.topol.2008.10.016 es_ES
dc.relation.references Ferrando J.C., Ka̧kol J.: A note on spaces C p (X) K-analytic-framed in $${\mathbb{R}^{X} }$$ . Bull. Aust. Math. Soc. 78, 141–146 (2008) es_ES
dc.relation.references Ferrando J.C., Ka̧kol J., López-Pellicer M.: Bounded tightness conditions and spaces C(X). J. Math. Anal. Appl. 297, 518–526 (2004) es_ES
dc.relation.references Ferrando J.C., Ka̧kol J., López-Pellicer M.: A characterization of trans-separable spaces. Bull. Belg. Math. Soc. Simon Stevin 14, 493–498 (2007) es_ES
dc.relation.references Ferrando, J.C., Ka̧kol, J., López-Pellicer, M.: Metrizability of precompact sets: an elementary proof. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A. Mat. RACSAM 99(2), 135–142 (2005). http://www.rac.es/ficheros/doc/00173.pdf es_ES
dc.relation.references Ferrando J.C., Ka̧kol J., López-Pellicer M., Saxon S.A.: Tightness and distinguished Fréchet spaces. J. Math. Anal. Appl. 324, 862–881 (2006). doi: 10.1016/j.jmaa.2005.12.059 es_ES
dc.relation.references Ferrando J.C., Ka̧kol J., López-Pellicer M., Saxon S.A.: Quasi-Suslin weak duals. J. Math. Anal. Appl. 339(2), 1253–1263 (2008). doi: 10.1016/j.jmaa.2007.07.081 es_ES
dc.relation.references Floret, K.: Weakly compact sets. Lecture Notes in Mathematics, vol. 801, Springer, Berlin (1980) es_ES
dc.relation.references Gillman L., Henriksen M.: Rings of continuous functions in which every finitely generated ideal is principial. Trans. Am. Math. Soc. 82, 366–391 (1956). doi: 10.2307/1993054 es_ES
dc.relation.references Gillman L., Jerison M.: Rings of Continuous Functions. Van Nostrand Reinhold Company, New York (1960) es_ES
dc.relation.references Grothendieck A.: Sur les applications linéaires faiblement compactes d’espaces du type C(K). Can. J. Math. 5, 129–173 (1953) es_ES
dc.relation.references Gullick D., Schmets J.: Separability and semi-norm separability for spaces of bounded continuous functions. Bull. R. Sci. Lige 41, 254–260 (1972) es_ES
dc.relation.references Hager A.W.: Some nearly fine uniform spaces. Proc. Lond. Math. Soc. 28, 517–546 (1974). doi: 10.1112/plms/s3-28.3.517 es_ES
dc.relation.references Howes N.R.: On completeness. Pacific J. Math. 38, 431–440 (1971) es_ES
dc.relation.references Isbell, J.R.: Uniform spaces. In: Mathematical Surveys 12, American Mathematical Society, Providence (1964) es_ES
dc.relation.references Ka̧kol J., López-Pellicer M.: Compact coverings for Baire locally convex spaces. J. Math. Anal. Appl. 332, 965–974 (2007). doi: 10.1016/j.jmaa.2006.10.045 es_ES
dc.relation.references Ka̧kol, J., López-Pellicer, M.: A characterization of Lindelöf Σ-spaces υ X (preprint) es_ES
dc.relation.references Ka̧kol J., López-Pellicer M., Śliwa W.: Weakly K-analytic spaces and the three-space property for analyticity. J. Math. Anal. Appl. 362(1), 90–99 (2010). doi: 10.1016/j.jmaa.2009.09.026 es_ES
dc.relation.references Ka̧kol J., Saxon S.: Montel (DF)-spaces, sequential (LM)-spaces and the strongest locally convex topology. J. Lond. Math. Soc. 66(2), 388–406 (2002) es_ES
dc.relation.references Ka̧kol J., Saxon S., Todd A.T.: Pseudocompact spaces X and df-spaces C c (X). Proc. Am. Math. Soc. 132, 1703–1712 (2004) es_ES
dc.relation.references Ka̧kol J., Śliwa W.: Strongly Hewitt spaces. Topology Appl. 119(2), 219–227 (2002). doi: 10.1016/S0166-8641(01)00063-3 es_ES
dc.relation.references Khan L.A.: Trans-separability in spaces of continuous vector-valued functions. Demonstr. Math. 37, 61–67 (2004) es_ES
dc.relation.references Khan L.A.: Trans-separability in the strict and compact-open topologies. Bull. Korean Math. Soc. 45, 681–687 (2008). doi: 10.4134/BKMS.2008.45.4.681 es_ES
dc.relation.references Khurana S.S.: Weakly compactly generated Fréchet spaces. Int. J. Math. Math. Sci. 2(4), 721–724 (1979). doi: 10.1155/S0161171279000557 es_ES
dc.relation.references Kirk R.B.: A note on the Mackey topology for (C b (X)*,C b (X)). Pacific J. Math. 45(2), 543–554 (1973) es_ES
dc.relation.references Köthe G.: Topological Vector Spaces I. Springer, Berlin (1969) es_ES
dc.relation.references Kubiś W., Okunev O., Szeptycki P.J.: On some classes of Lindelöf Σ-spaces. Topol. Appl. 153(14), 2574–2590 (2006). doi: 10.1016/j.topol.2005.09.009 es_ES
dc.relation.references Künzi H.P.A., Mršević M., Reilly I.L., Vamanamurthy M.K.: Pre-Lindelöf quasi-pseudo-metric and quasi-uniform spaces. Mat. Vesnik 46, 81–87 (1994) es_ES
dc.relation.references Megginson R.: An Introduction to Banach Space Theory. Springer, Berlin (1988) es_ES
dc.relation.references Michael E.: ℵ0-spaces. J. Math. Mech. 15, 983–1002 (1966) es_ES
dc.relation.references Nagami K.: Σ-spaces. Fund. Math. 61, 169–192 (1969) es_ES
dc.relation.references Narayanaswami P.P., Saxon S.A.: (LF)-spaces, quasi-Baire spaces and the strongest locally convex topology. Math. Ann. 274, 627–641 (1986). doi: 10.1007/BF01458598 es_ES
dc.relation.references Negrepontis S.: Absolute Baire sets. Proc. Am. Math. Soc. 18(4), 691–694 (1967). doi: 10.2307/2035440 es_ES
dc.relation.references Orihuela J.: Pointwise compactness in spaces of continuous functions. J. Lond. Math. Soc. 36(2), 143–152 (1987). doi: 10.1112/jlms/s2-36.1.143 es_ES
dc.relation.references Orihuela, J.: On weakly Lindelöf Banach spaces. In: Bierstedt, K.D. et al. (eds.) Progress in Functional Analysis, pp. 279–291. Elsvier, Amsterdam (1992). doi: 10.1016/S0304-0208(08)70326-8 es_ES
dc.relation.references Orihuela J., Schachermayer W., Valdivia M.: Every Readom–Nikodym Corson compact space is Eberlein compact. Stud. Math. 98, 157–174 (1992) es_ES
dc.relation.references Orihuela, J., Valdivia, M.: Projective generators and resolutions of identity in Banach spaces. Rev. Mat. Complut. 2(Supplementary Issue), 179–199 (1989) es_ES
dc.relation.references Pérez Carreras P., Bonet J.: Barrelled Locally Convex Spaces, Mathematics Studies 131. North-Holland, Amsterdam (1987) es_ES
dc.relation.references Pfister H.H.: Bemerkungen zum Satz über die separabilität der Fréchet-Montel Raüme. Arch. Math. (Basel) 27, 86–92 (1976). doi: 10.1007/BF01224645 es_ES
dc.relation.references Robertson N.: The metrisability of precompact sets. Bull. Aust. Math. Soc. 43(1), 131–135 (1991). doi: 10.1017/S0004972700028847 es_ES
dc.relation.references Rogers C.A., Jayne J.E., Dellacherie C., Topsøe F., Hoffman-Jørgensen J., Martin D.A., Kechris A.S., Stone A.H.: Analytic Sets. Academic Press, London (1980) es_ES
dc.relation.references Saxon S.A.: Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology. Math. Ann. 197(2), 87–106 (1972). doi: 10.1007/BF01419586 es_ES
dc.relation.references Schawartz L.: Radom Measures on Arbitrary Topological Spaces and Cylindrical Measures. Oxford University Press, Oxford (1973) es_ES
dc.relation.references Schlüchtermann G., Wheller R.F.: On strongly WCG Banach spaces. Math. Z. 199(3), 387–398 (1988). doi: 10.1007/BF01159786 es_ES
dc.relation.references Schlüchtermann G., Wheller R.F.: The Mackey dual of a Banach space. Note Math. 11, 273–287 (1991) es_ES
dc.relation.references Schmets, J.: Espaces de functions continues. Lecture Notes in Mathematics, vol 519, Springer-Verlag, Berlin-New York (1976) es_ES
dc.relation.references Talagrand M.: Sur une conjecture de H. H. Corson. Bull. Soc. Math. 99, 211–212 (1975) es_ES
dc.relation.references Talagrand M.: Espaces de Banach faiblement K-analytiques. Ann. Math. 110, 407–438 (1979) es_ES
dc.relation.references Talagrand M.: Weak Cauchy sequences in L 1(E). Am. J. Math. 106(3), 703–724 (1984). doi: 10.2307/2374292 es_ES
dc.relation.references Tkachuk V.V.: A space C p (X) is dominated by irrationals if and only if it is K-analytic. Acta Math. Hungar. 107(4), 253–265 (2005) es_ES
dc.relation.references Tkachuk V.V.: Lindelöf Σ-spaces: an omnipresent class. RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A. Mat. 104(2), 221–244 (2010). doi: 10.5052/RACSAM.2010.15 es_ES
dc.relation.references Todd A.R., Render H.: Continuous function spaces, (db)-spaces and strongly Hewitt spaces. Topol. Appl. 141, 171–186 (2004). doi: 10.1016/j.topol.2003.12.005 es_ES
dc.relation.references Valdivia M.: Topics in Locally Convex Spaces, Mathematics Studies 67. North-Holland, Amsterdam (1982) es_ES
dc.relation.references Valdivia M.: Espacios de Fréchet de generación débilmente compacta. Collect. Math. 38, 17–25 (1987) es_ES
dc.relation.references Valdivia M.: Resolutions of identity in certain Banach spaces. Collect. Math. 38, 124–140 (1988) es_ES
dc.relation.references Valdivia M.: Resolutions of identity in certain metrizable locally convex spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 83, 75–96 (1989) es_ES
dc.relation.references Valdivia M.: Projective resolutions of identity in C(K) spaces. Arch. Math. (Basel) 54, 493–498 (1990) es_ES
dc.relation.references Valdivia, M.: Resoluciones proyectivas del operador identidad y bases de Markusevich en ciertos espacios de Banach. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 84, 23–34 es_ES
dc.relation.references Valdivia M.: Quasi-LB-spaces. J. Lond. Math. Soc. 35(2), 149–168 (1987). doi: 10.1112/jlms/s2-35.1.149 es_ES
dc.relation.references Walker, R.C.: The Stone-Čech compactification Ergebnisse der Mathematik und ihrer Grenzgebiete. Band 83. Springer, Berlin (1974) es_ES


This item appears in the following Collection(s)

Show simple item record