does not imply .
Katetov Extension as a Functor.
Lipschitz extensions and Lipschitz retractions in metric spaces
Łukasiewicz tribes are absolutely sequentially closed bold algebras
We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean -algebra) can be uniquely extended to a sequentially continuous measure on the generated Łukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on Łukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields...
Magill-type theorems for mappings.
Measure and measurable functions of
Measure of nonhyperconvexity and fixed-point theorems.
Monotone extenders for bounded c-valued functions
Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, the set of all bounded continuous functions f: A → c, and the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...
Monotone normality and extension of functions
We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of -spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.
Mutational retracts and extensions of mutations
Note about atom-categories of topological spaces
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