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The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.

Some relations between shape constructions

Friedrich W. Bauer (1978)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Some relative properties on normality and paracompactness, and their absolute embeddings

Shinji Kawaguchi, Ryoken Sokei (2005)

Commentationes Mathematicae Universitatis Carolinae

Paracompactness ( $= 2$ -paracompactness) and normality of a subspace $Y$ in a space $X$ defined by Arhangel’skii and Genedi [4] are fundamental in the study of relative topological properties ([2], [3]). These notions have been investigated by primary using of the notion of weak $C$ - or weak $P$ -embeddings, which are extension properties of functions defined in [2] or [18]. In fact, Bella and Yaschenko [8] characterized Tychonoff spaces which are normal in every larger Tychonoff space, and this result is essentially...

Some remarks concerning the fundamental dimension of the cartesian product of two compacta

Sławomir Nowak (1979)

Fundamenta Mathematicae

Some remarks concerning the shape of pointed compacta

Karol Borsuk (1970)

Fundamenta Mathematicae

Some remarks on almost continuous functions

Zbigniew Piotrowski (1989)

Mathematica Slovaca

Some remarks on almost radiality in function spaces

Georgi D. Dimov, Gino Tironi (1987)

Acta Universitatis Carolinae. Mathematica et Physica

Some remarks on the product of two $C_{α}$ -compact subsets

Salvador García-Ferreira, Manuel Sanchis, Stephen W. Watson (2000)

Czechoslovak Mathematical Journal

For a cardinal $α$ , we say that a subset $B$ of a space $X$ is $C_{α}$ -compact in $X$ if for every continuous function $f X \to ℝ^{α}$ , $f [B]$ is a compact subset of $ℝ^{α}$ . If $B$ is a $C$ -compact subset of a space $X$ , then $ρ (B, X)$ denotes the degree of $C_{α}$ -compactness of $B$ in $X$ . A space $X$ is called $α$ -pseudocompact if $X$ is $C_{α}$ -compact into itself. For each cardinal $α$ , we give an example of an $α$ -pseudocompact space $X$ such that $X \times X$ is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...

Some remarks providing discontinuous maps on some $C_{p} (X)$ spaces

S. Moll (2008)

Banach Center Publications

Let X be a completely regular Hausdorff topological space and $C_{p} (X)$ the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space $C_{p} (X)$ , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of $C_{p} (X)$ .

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Some properties of the ideal of continuous functions with pseudocompact support.

Some properties of the induced map

Some properties of the remainder of Stone-Čech compactifications

Some properties of uniform ordered spaces

Some properties of weakly open functions in bitopological spaces.

Some qualitative problems in the theory of second order partial differential equations

Some questions on the composition factor property for atomic mappings.

Some recent results concerning weak Asplund spaces

Some refinements of a selection theorem with O-dimensional domain