A survey of Dugundji Extension Theory
A SURVEY OF SEMIGROUPS OF CONTINUOUS SELFMAPS.
A survey of various modifications of the notions of absolute retracts and absolute neighborhood retracts
A survey on topological games and their applications in analysis.
In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.
A suspension theorem for the proper homotopy and strong shape theories
A theorem of Borsuk-Ulam type for multifunctions
A theorem of the Hahn-Banach type and its applications
Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.
A theorem on mappings
A theorem on the weak topology of C(X) for compact scattered X
A theory of absolute proper retracts
A theory of proper shape for locally compact metric spaces
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset of the solution set of the singularly perturbed system. This subset is the set of...
A topological dichotomy with applications to complex analysis
Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the image f(∂D) of the boundary ∂D of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles,...
A topological lattice on the set of multifunctions.
A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement
We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.
A topological version of a combinatorial theorem of Katětov
A topology generated by eventually different functions
A topology on inequalities.
A Tychonoff non-normal space.
A Unified Theory of Perfect and Related Functions