On a generalization of Dugundji extension theorem
On a result of Adasch and Ernst.
On Absolutely Closed Multivalued Mappings of Topological Spaces
On continuous extension of uniformly continuous functions and metrics
We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
On Convex Sets with Convex-Hereditary CEP
CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.
On extending homeomorphisms on zero-dimensional spaces
On extending transitive homeomorphisms from the Cantor set to the product of two Cantor sets
On Extensions of Multivalued Mappings of Topological Spaces
On extensions of uniformly continuous Banach-space-valued mappings
On linear functorial operators extending pseudometrics
For a functor on the category of metrizable compacta, we introduce a conception of a linear functorial operator extending (for each ) pseudometrics from onto (briefly LFOEP for ). The main result states that the functor of -symmetric power admits a LFOEP if and only if the action of on has a one-point orbit. Since both the hyperspace functor and the probability measure functor contain as a subfunctor, this implies that both and do not admit LFOEP.
On minimal Hausdorff and minimal Urysohn functions
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
On non-separable 0-dimensional metrizable spaces
On open maps of Borel sets
We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.
On Stone extensions of homotopic maps
On the extension of continuous functions
On the Novák completion of convergence groups
On the -continuous fixed point property.
On transfinite sequences of mappings
On -embedded sets and extension of mappings
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
Openly factorizable spaces and compact extensions of topological semigroups
We prove that the semigroup operation of a topological semigroup extends to a continuous semigroup operation on its Stone-Čech compactification provided is a pseudocompact openly factorizable space, which means that each map to a second countable space can be written as the composition of an open map onto a second countable space and a map . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.