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As usual $C (X)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$ . It is well-known that if $X$ and $Y$ are realcompact spaces such that $C (X)$ and $C (Y)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C (X)$ determines $X$ . The restriction to realcompact spaces stems from the fact that $C (X)$ and $C (υ X)$ are isomorphic, where $υ X$ is the (Hewitt) realcompactification of $X$ . In this note, a class of locally compact spaces $X$ that includes properly the class of locally compact realcompact spaces is exhibited...

$C (X)$ in the weak topology.

Veličko, N.V. (1995)

Georgian Mathematical Journal

Canonical embedding of function spaces into the topological bidual of $𝐂 (K; E)$ .

Ngimbi, E.N. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Caractérisation topologique de l'espace des fonctions dérivables

Robert Cauty (1991)

Fundamenta Mathematicae

Carathéodory's selections for multifunctions with non-separable range

Biagio Ricceri (1982)

Rendiconti del Seminario Matematico della Università di Padova

Cardinal invariants of universals

Gareth Fairey, Paul Gartside, Andrew Marsh (2005)

Commentationes Mathematicae Universitatis Carolinae

We examine when a space $X$ has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the $σ$ -weight of $X$ when $X$ is perfectly normal. We also show that if $Y$ parametrises a zero set universal for $X$ then $h L (X^{n}) \leq h d (Y)$ for all $n \in ℕ$ . We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a $K$ -coarser topology. Examples are given including an $S$ space with zero set universal parametrised by an $L$ space (and...

Cardinal invariants of $λ$ -topologies.

Velichko, N.V. (2004)

Sibirskij Matematicheskij Zhurnal

Cartesian closed hull for metric spaces

Jiří Adámek, Jan Reiterman (1990)

Commentationes Mathematicae Universitatis Carolinae

Cartesian closed hull for (quasi-)metric spaces (revisited)

Mark Nauwelaerts (2000)

Commentationes Mathematicae Universitatis Carolinae

An existing description of the cartesian closed topological hull of $p {MET}^{\infty}$ , the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a “family” of cartesian closed topological subconstructs of $p q s {MET}^{\infty}$ , the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of...

Cartesian closed hull of uniform spaces

Adámek, Jiří, Reiterman, Jan (1981)

Abstracta. 9th Winter School on Abstract Analysis

Cartesian closed topological hull of the construct of closure spaces.

Claes, V., Lowen-Colebunders, E., Sonck, G. (2001)

Theory and Applications of Categories [electronic only]

Categories of Wallman extendible functions

Darrell W. Hajek (1977)

Compositio Mathematica

C-closed functions

G. L. Garg, B. Kumar (1989)

Matematički Vesnik

Čech methods and the adjoint functor theorem

Renato Betti (1985)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Čech-Stone-like compactifications for general topological spaces

Miroslav Hušek (1992)

Commentationes Mathematicae Universitatis Carolinae

The problem whether every topological space $X$ has a compactification $Y$ such that every continuous mapping $f$ from $X$ into a compact space $Z$ has a continuous extension from $Y$ into $Z$ is answered in the negative. For some spaces $X$ such compactifications exist.

Cellularity and the index of narrowness in topological groups

Mihail G. Tkachenko (2011)

Commentationes Mathematicae Universitatis Carolinae

We study relations between the cellularity and index of narrowness in topological groups and their $G_{δ}$ -modifications. We show, in particular, that the inequalities $in ({(H)}_{τ}) \leq 2^{τ \cdot in (H)}$ and $c ({(H)}_{τ}) \leq 2^{2^{τ \cdot in (H)}}$ hold for every topological group $H$ and every cardinal $τ \geq ω$ , where ${(H)}_{τ}$ denotes the underlying group $H$ endowed with the $G_{τ}$ -modification of the original topology of $H$ and $in (H)$ is the index of narrowness of the group $H$ . Also, we find some bounds for the complexity of continuous real-valued functions $f$ on an arbitrary $ω$ -narrow group $G$ understood...

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