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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.

Intuitionistic I -fuzzy topological spaces

Cong-hua Yan, Xiao-ke Wang (2010)

Czechoslovak Mathematical Journal

The main purpose of this paper is to introduce the concept of intuitionistic I -fuzzy quasi-coincident neighborhood systems of intuitiostic fuzzy points. The relation between the category of intuitionistic I -fuzzy topological spaces and the category of intuitionistic I -fuzzy quasi-coincident neighborhood spaces are studied. By using fuzzifying topology, the notion of generated intuitionistic I -fuzzy topology is proposed, and the connections among generated intuitionistic I -fuzzy topological spaces,...

Invariant Borel liftings for category algebras of Baire groups

Maxim R. Burke (2007)

Fundamenta Mathematicae

R. A. Johnson showed that there is no translation-invariant Borel lifting for the measure algebra of ℝ/ℤ equipped with Haar measure, a result which was generalized by M. Talagrand to non-discrete locally compact abelian groups and by J. Kupka and K. Prikry to arbitrary non-discrete locally compact groups. In this paper we study analogs of these results for category algebras (the Borel σ-algebra modulo the ideal of first category sets) of topological groups. Our main results are for the class of...

Invariant metrics on G -spaces

Bogusław Hajduk, Rafał Walczak (2003)

Czechoslovak Mathematical Journal

Let X be a G -space such that the orbit space X / G is metrizable. Suppose a family of slices is given at each point of X . We study a construction which associates, under some conditions on the family of slices, with any metric on X / G an invariant metric on X . We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.

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