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The class of quasi Radon-Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon-Nikodým compact spaces. Adapting Alster's proof we show that every quasi Radon-Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi Radon-Nikodým...

Some remarks on shape properties of compacta

Karol Borsuk (1974)

Fundamenta Mathematicae

Some remarks on subgroups of real numbers

Paul Erdös (1979)

Colloquium Mathematicae

Some remarks on Suslin sections

Gilles Godefroy (1986)

Studia Mathematica

Some remarks on Tardiff's fixed point theorem on Menger spaces.

Părău, E., Radu, V. (1997)

Portugaliae Mathematica

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 on the relation of classical set-valued mappings to the Baire classification

Kazimierz Kuratowski (1979)

Colloquium Mathematicum

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 $C_{p} (X)$ .

Some representations of midconvex set-valued functions.

K. Nikodem, F., Vercillo, S. Papalini (1997)

Aequationes mathematicae

Some results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

Commentationes Mathematicae Universitatis Carolinae

A space $X$ is truly weakly pseudocompact if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with $χ (x, X) > ω$ for every $x \in X$ ; (2) every locally bounded space is truly weakly pseudocompact; (3) for $ω < κ < α$ , the $κ$ -Lindelöfication of a discrete space of cardinality $α$ is weakly pseudocompact if $κ = κ^{ω}$ .

Some results for one class of discontinuous operators with fixed points.

Morales, R., Rojas, E. (2007)

Acta Mathematica Universitatis Comenianae. New Series

Some results in fixed point theory concerning generalized metric spaces

Ali Fora, Azzeddine Bellour, Adnan Al-Bsoul (2009)

Matematički Vesnik

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