- -

On realcompact topological vector spaces

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

On realcompact topological vector spaces

Mostrar el registro completo del ítem

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

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/75518

Ficheros en el ítem

Thumbnail
Nombre: JERZY KAKOL;López ...
Tamaño: 383.5Kb
Formato: PDF
Descripción: Versión editorial
Abrir/Preview

Metadatos del ítem

Título: On realcompact topological vector spaces
Autor: Kakol, Jerzy Marian López Pellicer, Manuel
Entidad UPV: Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural
Fecha difusión:
Resumen:
[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, ...[+]
Palabras clave: Angelicity , Baire and (b-) Baire-like , Bornological , Borel set , C*-embedded , Class B , (DF) space , Distinguished space , Frechet-Urysohn , k-Space , K-Analytic , (Weakly) Lindelof (Sigma) , Locally convex space , (Sigma-)Quasi-Suslin space , (Strongly) realcompact space , Talagrand compact , (Countable) tightness , Trans-separable , Weakly compact , (WCG) space , Web-bounded (compact)
Derechos de uso: Reconocimiento - No comercial (by-nc)
Fuente:
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. (issn: 1578-7303 ) (eissn: 1579-1505 )
DOI: 10.1007/s13398-011-0003-0
Editorial:
Springer
Versión del editor: https://dx.doi.org/10.1007/s13398-011-0003-0
Código del Proyecto:
info:eu-repo/grantAgreement/MNiSW//NN201 2740 33/
info:eu-repo/grantAgreement/MICINN//MTM2008-01502/ES/ELEMENTOS DE TOPOLOGIA DESCRIPTIVA DE CONJUNTOS EN ANALISIS FUNCIONAL LINEAL/
Agradecimientos:
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 ...[+]
Tipo: Artículo

References

Argyros S., Mercourakis S.: On weakly Lindelöf Banach spaces. Rocky Mountain J. Math. 23(2), 395–446 (1993). doi: 10.1216/rmjm/1181072569

Arkhangel’skii, A. V.: Topological Function Spaces, Mathematics and its Applications, vol. 78, Kluwer, Dordrecht (1992)

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) [+]
Argyros S., Mercourakis S.: On weakly Lindelöf Banach spaces. Rocky Mountain J. Math. 23(2), 395–446 (1993). doi: 10.1216/rmjm/1181072569

Arkhangel’skii, A. V.: Topological Function Spaces, Mathematics and its Applications, vol. 78, Kluwer, Dordrecht (1992)

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)

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

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)

Cascales B.: On K-analytic locally convex spaces. Arch. Math. 49, 232–244 (1987)

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

Cascales B., Ka̧kol J., Saxon S.A.: Metrizability vs. Fréchet–Urysohn property. Proc. Am. Math. Soc. 131, 3623–3631 (2003)

Cascales B., Namioka I., Orihuela J.: The Lindelöf property in Banach spaces. Stud. Math. 154, 165–192 (2003). doi: 10.4064/sm154-2-4

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

Cascales B., Orihuela J.: On compactness in locally convex spaces, Math. Z. 195(3), 365–381 (1987). doi: 10.1007/BF01161762

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

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

van Douwen E.K.: Prime mappings, number of factors and binary operations. Dissertationes Math. (Rozprawy Mat.) 199, 35 (1981)

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

Engelking R.: General Topology. Heldermann Verlag, Lemgo (1989)

Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, J., Zizler, V.: Functional Analysis and Infinite-Dimensional Geometry. Canadian Mathematical Society. Springer, Berlin (2001)

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

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

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)

Ferrando J.C., Ka̧kol J., López-Pellicer M.: Bounded tightness conditions and spaces C(X). J. Math. Anal. Appl. 297, 518–526 (2004)

Ferrando J.C., Ka̧kol J., López-Pellicer M.: A characterization of trans-separable spaces. Bull. Belg. Math. Soc. Simon Stevin 14, 493–498 (2007)

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

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

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

Floret, K.: Weakly compact sets. Lecture Notes in Mathematics, vol. 801, Springer, Berlin (1980)

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

Gillman L., Jerison M.: Rings of Continuous Functions. Van Nostrand Reinhold Company, New York (1960)

Grothendieck A.: Sur les applications linéaires faiblement compactes d’espaces du type C(K). Can. J. Math. 5, 129–173 (1953)

Gullick D., Schmets J.: Separability and semi-norm separability for spaces of bounded continuous functions. Bull. R. Sci. Lige 41, 254–260 (1972)

Hager A.W.: Some nearly fine uniform spaces. Proc. Lond. Math. Soc. 28, 517–546 (1974). doi: 10.1112/plms/s3-28.3.517

Howes N.R.: On completeness. Pacific J. Math. 38, 431–440 (1971)

Isbell, J.R.: Uniform spaces. In: Mathematical Surveys 12, American Mathematical Society, Providence (1964)

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

Ka̧kol, J., López-Pellicer, M.: A characterization of Lindelöf Σ-spaces υ X (preprint)

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

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)

Ka̧kol J., Saxon S., Todd A.T.: Pseudocompact spaces X and df-spaces C c (X). Proc. Am. Math. Soc. 132, 1703–1712 (2004)

Ka̧kol J., Śliwa W.: Strongly Hewitt spaces. Topology Appl. 119(2), 219–227 (2002). doi: 10.1016/S0166-8641(01)00063-3

Khan L.A.: Trans-separability in spaces of continuous vector-valued functions. Demonstr. Math. 37, 61–67 (2004)

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

Khurana S.S.: Weakly compactly generated Fréchet spaces. Int. J. Math. Math. Sci. 2(4), 721–724 (1979). doi: 10.1155/S0161171279000557

Kirk R.B.: A note on the Mackey topology for (C b (X)*,C b (X)). Pacific J. Math. 45(2), 543–554 (1973)

Köthe G.: Topological Vector Spaces I. Springer, Berlin (1969)

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

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)

Megginson R.: An Introduction to Banach Space Theory. Springer, Berlin (1988)

Michael E.: ℵ0-spaces. J. Math. Mech. 15, 983–1002 (1966)

Nagami K.: Σ-spaces. Fund. Math. 61, 169–192 (1969)

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

Negrepontis S.: Absolute Baire sets. Proc. Am. Math. Soc. 18(4), 691–694 (1967). doi: 10.2307/2035440

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

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

Orihuela J., Schachermayer W., Valdivia M.: Every Readom–Nikodym Corson compact space is Eberlein compact. Stud. Math. 98, 157–174 (1992)

Orihuela, J., Valdivia, M.: Projective generators and resolutions of identity in Banach spaces. Rev. Mat. Complut. 2(Supplementary Issue), 179–199 (1989)

Pérez Carreras P., Bonet J.: Barrelled Locally Convex Spaces, Mathematics Studies 131. North-Holland, Amsterdam (1987)

Pfister H.H.: Bemerkungen zum Satz über die separabilität der Fréchet-Montel Raüme. Arch. Math. (Basel) 27, 86–92 (1976). doi: 10.1007/BF01224645

Robertson N.: The metrisability of precompact sets. Bull. Aust. Math. Soc. 43(1), 131–135 (1991). doi: 10.1017/S0004972700028847

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)

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

Schawartz L.: Radom Measures on Arbitrary Topological Spaces and Cylindrical Measures. Oxford University Press, Oxford (1973)

Schlüchtermann G., Wheller R.F.: On strongly WCG Banach spaces. Math. Z. 199(3), 387–398 (1988). doi: 10.1007/BF01159786

Schlüchtermann G., Wheller R.F.: The Mackey dual of a Banach space. Note Math. 11, 273–287 (1991)

Schmets, J.: Espaces de functions continues. Lecture Notes in Mathematics, vol 519, Springer-Verlag, Berlin-New York (1976)

Talagrand M.: Sur une conjecture de H. H. Corson. Bull. Soc. Math. 99, 211–212 (1975)

Talagrand M.: Espaces de Banach faiblement K-analytiques. Ann. Math. 110, 407–438 (1979)

Talagrand M.: Weak Cauchy sequences in L 1(E). Am. J. Math. 106(3), 703–724 (1984). doi: 10.2307/2374292

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)

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

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

Valdivia M.: Topics in Locally Convex Spaces, Mathematics Studies 67. North-Holland, Amsterdam (1982)

Valdivia M.: Espacios de Fréchet de generación débilmente compacta. Collect. Math. 38, 17–25 (1987)

Valdivia M.: Resolutions of identity in certain Banach spaces. Collect. Math. 38, 124–140 (1988)

Valdivia M.: Resolutions of identity in certain metrizable locally convex spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 83, 75–96 (1989)

Valdivia M.: Projective resolutions of identity in C(K) spaces. Arch. Math. (Basel) 54, 493–498 (1990)

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

Valdivia M.: Quasi-LB-spaces. J. Lond. Math. Soc. 35(2), 149–168 (1987). doi: 10.1112/jlms/s2-35.1.149

Walker, R.C.: The Stone-Čech compactification Ergebnisse der Mathematik und ihrer Grenzgebiete. Band 83. Springer, Berlin (1974)

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem