Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T21:22:59.640Z Has data issue: false hasContentIssue false
  • English
  • Français

On metrizable E with Cp(E) ≇ Cp(E) × Cp(E)

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  26 February 2010

Roman Pol
Roman Pol
Affiliation:
Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland.
Get access

Extract

Given a topological space X, we denote by Cp(X) the space of real-valued continuous functions on X, equipped with the topology of pointwise convergence.

MSC classification

Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 49 - 55
Copyright
Copyright © University College London 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

A1.Aleksandrov, P. S.. On countable-to-one open mappings. Dokl. Akad. Nauk SSSR, 7 (1936), 283–287 (in Russian).Google Scholar
Ar 1.Arkhangel'skiľ, A. V.. Problems in C p-theory. In Open Problems in Topology, editors van Mill, J., G. M. Reed (North-Holland, 1990).Google Scholar
Ar 2.Arkhangel'skiľ, A. V.. C p-Theory. In Recent Progress in General Topology, editors Husek, M. and van Mill, J. (North-Holland, 1992).Google Scholar
Ar 3.Arkhangel'skiľ, A. V.. On linear homeomorphisms of function spaces. Soviet Math. Dokl., 25 (1982), 852–855.Google Scholar
B-dG.Baars, J. and de Groot, J.. On topological and linear equivalence of certain function spaces (Centrum voor Wiskunde en Informatica, 1990).Google Scholar
B-dG-P.Baars, J., de Groot, J. and Pelant, J.. Function spaces of completely metrizable spaces. Trans. Amer. Math. Soc, 140 (1993), 871–883.CrossRefGoogle Scholar
Ba.Baumgartner, J.. All Ni-dense sets of reals can be isomorphic. Fund. Math., 89 (1973), 101–106.CrossRefGoogle Scholar
Co.Cook, H.. Continua which admit only the identity mapping onto non-degenerate subcontinua. Fund. Math., 60 (1967), 241–249.CrossRefGoogle Scholar
Ku 1.Kuratowski, K.. Sur la puissance de l'ensemble des “nombres de dimension” au sens de M. Frechet. Fund. Math., 8 (1926), 201–208.CrossRefGoogle Scholar
Ku 2.Kuratowski, K.. Topology, Vol. I (PWN & Academic Press, 1966).Google Scholar
K-M.Kuratowski, K. and Mostowski, A.. Set theory (PWN ' North-Holland, 1976).Google Scholar
Po 1.Pol, R.. Note on decompositions of metrizable spaces I. Fund. Math., 95 (1977), 95–103.CrossRefGoogle Scholar
Po 2.Pol, R.. Note on decompositions of metrizable spaces II. Fund. Math., 100 (1978), 129–143.CrossRefGoogle Scholar
St.Stone, A. H.. On a-discreteness and Borel isomorphism. Amer. J. Math., 85 (1963), 655–666.CrossRefGoogle Scholar