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Ideals of uniformly continuous mappings on pseudometric spaces

Jan Pelant, Jiří Vilímovský (1986)

Commentationes Mathematicae Universitatis Carolinae

In search for Lindelöf $C_{p}$ ’s

Raushan Z. Buzyakova (2004)

Commentationes Mathematicae Universitatis Carolinae

It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_{p} (X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_{p} (X)$ is less than the Lindelöf number of $C_{p} (X)$ . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.

Indicatrix of Banach and a Space of Continuous Functions

Pavel Kostyrko (1969)

Matematický časopis

Intégrité du complété et théorème de Stone-Weierstrass

Paul-Jean Cahen, Fulvio Grazzini, Youssef Haouat (1982)

Annales scientifiques de l'Université de Clermont. Mathématiques

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan (1998)

Serdica Mathematical Journal

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first...

Iterated and double limits

Paul R. Beesack (1986)

Annales Polonici Mathematici