On the property (db) for continuous function spaces

It is shown that the space C( X) of all continuous real-valued functions with the compact-open topology has the property (db) iff X is a μ-space and a τα-space. As a consequence C( X) has the property (db) iff C( X) is Baire-like answering a question in the literature. Generalizations to the topolog...

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Vydáno v:Topology and its applications Ročník 92; číslo 2; s. 101 - 106
Hlavní autor: Render, Hermann
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 1999
Témata:
Baire-like spaces
Continuous function spaces
db-spaces
Baire-like spaces
db-spaces
54E52
54C35
Continuous function spaces
ISSN:0166-8641, 1879-3207
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Shrnutí:It is shown that the space C( X) of all continuous real-valued functions with the compact-open topology has the property (db) iff X is a μ-space and a τα-space. As a consequence C( X) has the property (db) iff C( X) is Baire-like answering a question in the literature. Generalizations to the topology of bounded convergence are given.
ISSN:0166-8641
1879-3207
DOI:10.1016/S0166-8641(97)00235-6