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A NOTE ON SPACES Cp(X)K-ANALYTIC-FRAMED IN ℝX

Part of: Maps and general types of spaces defined by maps Connections with other structures, applications

Published online by Cambridge University Press:  01 August 2008

J. C. FERRANDO  and
J. KĄKOL
J. C. FERRANDO*
Affiliation:
Centro de Investigación Operativa, Universidad Miguel Hernández, E-03202 Elche (Alicante), Spain (email: [email protected])
J. KĄKOL
Affiliation:
Faculty of Mathematics and Informatics, A. Mickiewicz University, 61-614 Poznań, Poland (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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This paper characterizes the K-analyticity-framedness in ℝX for Cp(X) (the space of real-valued continuous functions on X with pointwise topology) in terms of Cp(X). This is used to extend Tkachuk’s result about the K-analyticity of spaces Cp(X) and to supplement the Arkhangel ′skiĭ–Calbrix characterization of σ-compact cosmic spaces. A partial answer to an Arkhangel ′skiĭ–Calbrix problem is also provided.

Keywords

P-framed spacecosmic spaceK-analytic spaceLindelöf Σ-spaceangelic space

MSC classification

Secondary: 54C35: Function spaces 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 141 - 146
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The research of both authors has been supported by project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the European Community (Feder funds). The second named author was also supported by grant MNiSW Nr. N N201 2740 33 as well as by the Technical University of Valencia (September 2007) with the grant ‘Ayuda para estancias de investigadores de prestigio en la UPV’.

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