Effective descent maps of topological spaces

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.

Spaces of Maps into Topological Group with the Whiteny Topology

Let X be a separable locally compact metrizable space and G a separable completely metrizable ANR topological group without isolated points. By C(X, G), we denote the topological group of all continuous maps f : X → G endowed with the Whitney (graph) topology and by Cc(X, G) the subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete then the spac...

Biequivariant Maps on Spheres and Topological Complexity of Lens Spaces

Weighted cup-length calculations in singular cohomology led Farber and Grant in 2008 to general lower bounds for the topological complexity of lens spaces. We replace singular cohomology by connective complex K-theory, and weighted cup-length arguments by considerations with biequivariant maps on spheres to improve on Farber–Grant’s bounds by arbitrarily large amounts. Our calculations are base...

σ-Normality of Topological Spaces

Fixed Points of Condensing Multivalued Maps in Topological Vector Spaces

The Schauder conjecture that every continuous single-valued map from a compact convex subset of a topological vector space into itself has a fixed point was stated in [12, Problem 54]. In a recent year, Cauty [2] gave a positive answer to this question by a very complicated approximation factorization. Very recently, Dobrowolski [3] established Cauty’s proof in a more accessible form by using t...