- -

A note on the weak topology of spaces Ck (X) of continuous functions

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A note on the weak topology of spaces Ck (X) of continuous functions

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: KakolMoll - A note ...
Tamaño: 361.4Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: Ka-kol_et_al-2021 ...
Tamaño: 291.1Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Kakol, Jerzy es_ES
dc.contributor.author Moll López, Santiago Emmanuel es_ES
dc.date.accessioned 2023-09-21T18:04:40Z
dc.date.available 2023-09-21T18:04:40Z
dc.date.issued 2021-07 es_ES
dc.identifier.issn 1578-7303 es_ES
dc.identifier.uri http://hdl.handle.net/10251/196896
dc.description.abstract [EN] It is well known that the property of being a bounded set in the class of topological vector spaces E is not a topological property, where a subset B ¿ E is called a bounded set if every neighbourhood of zero U in E absorbs B. The paper deals with the problem which topological properties of bounded sets for the space Ck (X) (of continuous real-valued functions on a Tychonoff space X with the compact-open topology) endowed with the weak topology of Ck (X) can be transferred to bounded sets of Ck (Y) endowed with the weak topology, assuming that the corresponding weak topologies of both Ck (X) and Ck (Y) are homeomorphic. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Baire and hereditary Baire space es_ES
dc.subject Bounded subset es_ES
dc.subject Compact and compact scattered es_ES
dc.subject Homeomorphism and linear homeomorphism es_ES
dc.subject Spaces of continuous functions es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A note on the weak topology of spaces Ck (X) of continuous functions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s13398-021-01051-1 es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería del Diseño - Escola Tècnica Superior d'Enginyeria del Disseny es_ES
dc.description.bibliographicCitation Kakol, J.; Moll López, SE. (2021). A note on the weak topology of spaces Ck (X) of continuous functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 115(3):1-10. https://doi.org/10.1007/s13398-021-01051-1 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s13398-021-01051-1 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 10 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 115 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\438376 es_ES
dc.description.references Arkhangel’skiĭ, A.V.: Topological function spaces. Math. and its Applications, vol. 78. Kluwer Academic Publishers, Dordrecht, Boston, London (1992) es_ES
dc.description.references Banach, S.: Théorie des oprérations linéaires. PWN, Warsaw (1932) es_ES
dc.description.references Banakh, T.: On Topological classification of normed spaces endowed with the weak topology of the topology of compact convergence. In: Banakh, T. (ed.) General Topology in Banach Spaces, pp. 171–178 . Nova Sci. Publ. (2001). arXiv:1908.09115v1 es_ES
dc.description.references Banakh, T.: $$k$$-scattered spaces (2020). arXiv:1904.08969v1 es_ES
dc.description.references Banakh, T., Kakol, J., Śliwa, W.: Josefson–Nissenzweig property for $$C_{p}$$-spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3015–3030 (2019). https://doi.org/10.1007/s13398-019-00667-8 es_ES
dc.description.references Bessaga, Cz., Pełczyński, A.: Spaces of continuous functions (IV) (On isomorphical classification of spaces of continuous functions). Studia Math. 73, 53–62 (1960) es_ES
dc.description.references Bierstedt, D., Bonet, J.: Density conditions in Fréchet and $$(DF)$$-spaces. Rev. Mat. Complut. 2, 59–75 (1989) es_ES
dc.description.references Bierstedt, D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. RACSAM. 97, 159–188 (2003) es_ES
dc.description.references Edgar, G.A., Wheller, R.F.: Topological properies of Banach spaces. Pac. J. Math. 115, 317–350 (1984) es_ES
dc.description.references Engelking, R.: General Topology. Heldermann Verlag, Berlin (1989) es_ES
dc.description.references Fabian, M., Habala, P., Hàjek, P., Montesinos, V., Pelant, J., Zizler, V.: Functional Analysis and Infinite-Dimensional Geometry. CMS Books Math./Ouvrages Math, SMC (2001) es_ES
dc.description.references Ferrando, J.C., Ka̧kol, J.: On precompact sets in spaces $$C_{c}\left( X\right)$$. Georg. Math. J. 20, 247–254 (2013) es_ES
dc.description.references Ferrando, J.C., Ka̧kol, J.: Metrizable Bounded Sets in $$C(X)$$ Spaces and Distinguished $$C_p(X)$$ Spaces. J. Convex Anal. 26, 1337–1346 (2019) es_ES
dc.description.references Ferrando, J.C., Gabriyelyan, S., Ka̧kol, J.: Bounded sets structure of $$C_p(X)$$ and quasi-(DF)-spaces. Math. Nachr. 292, 2602–2618 (2019) es_ES
dc.description.references Ferrando, J.C.: Descriptive topology for analysts. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(2), 34 (2020). https://doi.org/10.1007/s13398-020-00837-z(Paper No. 107) es_ES
dc.description.references Ferrando, J.C., Kakol, J., Leiderman, A., Saxon, S.: Distinguished Cp(X) spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115(1), 18 (2021). https://doi.org/10.1007/s13398-020-00967-4 (Paper No. 27) es_ES
dc.description.references Fréchet, M.: Les espaces abstraits. Hermann, Paris (1928) es_ES
dc.description.references Gabriyelyan, S., Ka̧kol, J., Kubzdela, A., Lopez Pellicer, M.: On topological properties of Fréchet locally convex spaces with the weak topology. Topol. Appl. 192, 123–137 (2015) es_ES
dc.description.references Gabriyelyan, S., Ka̧kol, J., Kubis, W., Marciszewski, W.: Networks for the weak topology of Banach and Fréchet spaces. J. Math. Anal. Appl. 432, 1183–1199 (2015) es_ES
dc.description.references Guerrero Sánchez, D.: Spaces with an M-diagonal. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(1), 9 (2020). https://doi.org/10.1007/s13398-019-00745-x (paper No. 16) es_ES
dc.description.references Jarchow, H.: Locally Convex Spaces. B.G. Teubner, Stuttgart (1981) es_ES
dc.description.references Kadec, M.I.: A proof of the topological equivalence of all separable infinite-dimensional Banach spaces. Funk. Anal. i Prilozen. 1, 61–70 (1967) es_ES
dc.description.references Ka̧kol, J., Saxon, S.A., Tood, A.: Pseudocompact spaces $$X$$ and $$df$$-spaces $$C_{c}(X)$$. Proc. Am. Math. Soc. 132, 1703–1712 (2004) es_ES
dc.description.references Ka̧kol, J., Kubiś, W., Lopez-Pellicer, M.: Descriptive Topology in Selected Topics of Functional Analysis. Developments in Mathematics. Springer, New York (2011) es_ES
dc.description.references Katetov, M.: On mappings of countable spaces. Colloq. Math. 2, 30–33 (1949) es_ES
dc.description.references Krupski, M., Marciszewski, W.: On the weak and pointwise topologies in function spaces II. J. Math. Anal. Appl. 452, 646–658 (2017) es_ES
dc.description.references Michael, E.: $$\aleph _{0}$$-spaces. J. Math. Mech. 15, 983–1002 (1966) es_ES
dc.description.references Miljutin, A.A.: Isomorphisms of the space of continuous functions over compact sets of the carinality of the continuum (Russian). Teor. Func. Anal. i PPrilozen. 2, 150–156 (1966) es_ES
dc.description.references Pełczyński, A., Semadeni, Z.: Spaces of continuous functions. III. Spaces $$C(\Omega )$$ for $$\Omega $$ without perfect subsets. Studia Math. 18, 211–222 (1959) es_ES
dc.description.references Pérez Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces. North-Holland Mathematics Studies, vol. 131. North-Holland, Amsterdam (1987) es_ES
dc.description.references Ruess, W.: Locally Convex Spaces not containing $$\ell _{1}$$. Funct. Approx. 50, 389–399 (2014) es_ES
dc.description.references Schlüchterman, G., Whiller, R.F.: The Mackey dual of a Banach space. Note di Mat. 11, 273–281 (1991) es_ES
dc.description.references Semadeni, Z.: Banach Spaces of Continuous Functions. PWN, Warsaw (1971) es_ES
dc.description.references Tkachuk, V.V.: Growths over discretes: some applications. Vestnik Mosk. Univ. Mat. Mec. 45(4), 19–21 (1990) es_ES
dc.description.references Tkachuk, V.V.: A $$C_p$$-Theory Problem Book. Special Features of Function Spaces. Problem Books in Mathematics. Springer, Cham (2014) es_ES
dc.description.references Toruńczyk, H.: Characterizing Hilbert space topology. Fund. Math. 111, 247–262 (1981) es_ES
dc.description.references Warner, S.: The topology of compact convergence on continuous functions spaces. Duke Math. J. 25, 265–282 (1958) es_ES


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

Mostrar el registro sencillo del ítem