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Ideal Banach category theorems and functions

Zbigniew Piotrowski (1997)

Mathematica Bohemica

Based on some earlier findings on Banach Category Theorem for some “nice” σ -ideals by J. Kaniewski, D. Rose and myself I introduce the h operator ( h stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained in this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of h -continuity. Results of this type lead, in the case of the σ -ideal of meager sets, to important statements...

Induced almost continuous functions on hyperspaces

Alejandro Illanes (2006)

Colloquium Mathematicae

For a metric continuum X, let C(X) (resp., 2 X ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and 2 f : 2 X → 2 Y be the induced functions given by C ( f ) ( A ) = c l Y ( f ( A ) ) and 2 f ( A ) = c l Y ( f ( A ) ) . In this paper, we prove that: • If 2 f is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1] such that...

Induced near-homeomorphisms

Włodzimierz J. Charatonik (2000)

Commentationes Mathematicae Universitatis Carolinae

We construct examples of mappings f and g between locally connected continua such that 2 f and C ( f ) are near-homeomorphisms while f is not, and 2 g is a near-homeomorphism, while g and C ( g ) are not. Similar examples for refinable mappings are constructed.

Is the product of ccc spaces a ccc space?

Nina M. Roy (1989)

Publicacions Matemàtiques

In this expository paper it is shown that Martin's Axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space. The Continuum Hypothesis is then used to construct the Laver-Gavin example of two ccc spaces whose product is not a ccc space.

Isometry groups of non standard metric products

Bogdana Oliynyk (2013)

Open Mathematics

We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.

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