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F σ -absorbing sequences in hyperspaces of subcontinua

Helma Gladdines (1993)

Commentationes Mathematicae Universitatis Carolinae

Let 𝒟 denote a true dimension function, i.e., a dimension function such that 𝒟 ( ℝ n ) = n for all n . For a space X , we denote the hyperspace consisting of all compact connected, non-empty subsets by C ( X ) . If X is a countable infinite product of non-degenerate Peano continua, then the sequence ( 𝒟 ≥ n ( C ( X ) ) ) n = 2 ∞ is F σ -absorbing in C ( X ) . As a consequence, there is a homeomorphism h : C ( X ) → Q ∞ such that for all n , h [ { A ∈ C ( X ) : 𝒟 ( A ) ≥ n + 1 } ] = B n × Q × Q × ⋯ , where B denotes the pseudo boundary of the Hilbert cube Q . It follows that if X is a countable infinite product of non-degenerate...

F σ -mappings and the invariance of absolute Borel classes

Petr Holický, Jiří Spurný (2004)

Fundamenta Mathematicae

It is proved that F σ -mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any F σ -mapping f: X → Y of an absolute Suslin metric space X onto an absolute Suslin metric space Y becomes a piecewise perfect mapping when restricted to a suitable F σ -set X ∞ ⊂ X satisfying f ( X ∞ ) = Y .

Factorizations of normality via generalizations of β -normality

Ananga Kumar Das, Pratibha Bhat, Ria Gupta (2016)

Mathematica Bohemica

The notion of β -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost β -normal spaces, which is a simultaneous generalization of β -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak β -normality, in terms of θ -closed sets, which turns out to be a simultaneous generalization of β -normality and θ -normality. A space X is said to be weakly β -normal (w β -normal ) if for every pair of disjoint...

Factorizations of set-valued mappings with separable range

Valentin G. Gutev (1996)

Commentationes Mathematicae Universitatis Carolinae

Right factorizations for a class of l.s.cṁappings with separable metrizable range are constructed. Besides in the selection and dimension theories, these l.s.cḟactorizations are also successful in solving the problem of factorizing a class of u.s.cṁappings.

Factorwise rigidity of embeddings of products of pseudo-arcs

Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel (2012)

Colloquium Mathematicae

An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc, then X ×...

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