A contribution to the topological classification of the spaces Ср(X)

Robert Cauty; Tadeusz Dobrowolski; Witold Marciszewski

ArticleOriginal scientific text

Title

A contribution to the topological classification of the spaces Ср(X)

Authors ¹, ², ³

Affiliations

Université Paris VI, Analyse Complexe et Géométrie, 4, Place Jussieu, 75252 Paris Cedex 05, France
Department of Mathematics, The University of Oklahoma, 601 Elm Avenue, Room 423, Norman, Oklahoma 73019-0315, U.S.A.
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

We prove that for each countably infinite, regular space X such that

C_{p} (X)

is a

Z_{σ}

-space, the topology of

C_{p} (X)

is determined by the class

F_{0} (C_{p} (X))

of spaces embeddable onto closed subsets of

C_{p} (X)

. We show that

C_{p} (X)

, whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set

Ω_{α}

for the multiplicative Borel class

M_{α}

if

F_{0} (C_{p} (X)) = M_{α}

. For each ordinal α ≥ 2, we provide an example

X_{α}

such that

C_{p} (X_{α})

is homeomorphic to

Ω_{α}

.

Keywords

ENG

function space, pointwise convergence topology, absorbing sets, Borel and projective filters

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http://matwbn.icm.edu.pl/ksiazki/fm/fm142/fm14236.pdf

Title

A contribution to the topological classification of the spaces Ср(X)

Affiliations

Abstract

Keywords

Bibliography

Additional information