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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.

Classical-type characterizations of non-metrizable ANE(n)-spaces

Valentin Gutev, Vesko Valov (1994)

Fundamenta Mathematicae

The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is L C n - 1 C n - 1 (resp., L C n - 1 ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

Continuous functions between Isbell-Mrówka spaces

Salvador García-Ferreira (1998)

Commentationes Mathematicae Universitatis Carolinae

Let Ψ ( Σ ) be the Isbell-Mr’owka space associated to the M A D -family Σ . We show that if G is a countable subgroup of the group 𝐒 ( ω ) of all permutations of ω , then there is a M A D -family Σ such that every f ∈ G can be extended to an autohomeomorphism of Ψ ( Σ ) . For a M A D -family Σ , we set I n v ( Σ ) = { f ∈ 𝐒 ( ω ) : f [ A ] ∈ Σ for all A ∈ Σ } . It is shown that for every f ∈ 𝐒 ( ω ) there is a M A D -family Σ such that f ∈ I n v ( Σ ) . As a consequence of this result we have that there is a M A D -family Σ such that n + A ∈ Σ whenever A ∈ Σ and n < ω , where n + A = { n + a : a ∈ A } for n < ω . We also notice that there is no M A D -family Σ such...

Continuous selections and approximations in α-convex metric spaces

A. Kowalska (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.

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