PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 153 | 2 | 125-40
Tytuł artykułu

A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions $c_p(X)$ onto $c_p(X)$ × ℝ$. In particular, $c_p(X)$ is not linearly homeomorphic to $c_p(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel'skiĭ.
Rocznik
Tom
153
Numer
2
Strony
125-40
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-01
poprawiono
1997-03-03
Twórcy
  • Faculty of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands, wmarcisz@mimuw.edu.pl
  • Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [Ar1] A. V. Arkhangel'skiĭ, Linear homeomorphisms of function spaces, Soviet Math. Dokl. 25 (3) (1982), 852-855.
  • [Ar2] A. V. Arkhangel'skiĭ, A survey of $C_p$-theory, Questions Answers Gen. Topology 5 (1987), 1-109.
  • [Ar3] A. V. Arkhangel'skiĭ, Problems in $C_p$-Theory, in: Open Problems in Topology, North-Holland, 1990, 601-615.
  • [Ar4] A. V. Arkhangel'skiĭ, $C_p$-theory, in: Recent Progress in General Topology, North-Holland, 1992, 1-56.
  • [BdG] J. Baars and J. de Groot, On Topological and Linear Equivalence of Certain Function Spaces, CWI Tract 86, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1992.
  • [Ber] Yu. F. Bereznitskiĭ, Nonhomeomorphism between two bicompacta, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 26 (6) (1971), 8-10 (in Russian).
  • [Be] C. Bessaga, A Lipschitz invariant of normed linear spaces related to the entropy numbers, Rocky Mountain J. Math. 10 (1980), 81-84.
  • [BPR] C. Bessaga, A. Pełczyński and S. Rolewicz, On diametral approximative dimension and linear homogeneity of F-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 677-683.
  • [Du] E. Dubinsky, Every separable Fréchet space contains a non-stable dense subspace, Studia Math. 40 (1971), 77-79.
  • [Go] W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), 523-530.
  • [GM] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
  • [Gu] S. P. Gul'ko, Spaces of continuous functions on ordinals and ultrafilters, Mat. Zametki 47 (4) (1990), 26-34 (in Russian).
  • [Kun] K. Kunen, Weak P-points in N*, in: Colloq. Math. Soc. János Bolyai 23, North-Holland, 1978, 741-749.
  • [Ku] K. Kuratowski, Sur la puissance de l'ensemble des "nombres de dimension" au sens de M. Fréchet, Fund. Math. 8 (1926), 201-208.
  • [KS] K. Kuratowski et W. Sierpiński, Sur un problème de M. Fréchet concernant les dimensions des ensembles linéaires, Fund. Math. 8 (1926), 193-200.
  • [Ma1] W. Marciszewski, A pre-Hilbert space without any continuous map onto its own square, Bull. Polish Acad. Sci. Math. 31 (1983), 393-397.
  • [Ma2] W. Marciszewski, A function space C(K) not weakly homeomorphic to C(K) × C(K), Studia Math. 88 (1988), 129-137.
  • [Ma3] W. Marciszewski, On van Mill's example of a normed X with $X ≉ X × ℝ$, preprint.
  • [vM1] J. van Mill, An introduction to ℝ, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 503-567.
  • [vM2] J. van Mill, Domain invariance in infinite-dimensional linear spaces, Proc. Amer. Math. Soc. 101 (1987), 173-180.
  • [Po1] R. Pol, An infinite-dimensional pre-Hilbert space not homeomorphic to its own square, Proc. Amer. Math. Soc. 90 (1984), 450-454.
  • [Po2] R. Pol, On metrizable E with $C_p(E) ≇ C_p(E) × C_p(E)$, Mathematika 42 (1995), 49-55.
  • [Ro] S. Rolewicz, An example of a normed space non-isomorphic to its product by the real line, Studia Math. 40 (1971), 71-75.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv153i2p125bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.