We prove that an -additive cover of a Čech complete, or more generally scattered-K-analytic space, has a σ-scattered refinement. This generalizes results of G. Koumoullis and R. W. Hansell.
It is proved that -mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any -mapping f: X → Y of an absolute Suslin metric space X onto an absolute Suslin metric space Y becomes a piecewise perfect mapping when restricted to a suitable -set satisfying .
In [2], D. E. Grow and M. Insall construct a countable compact set which is not the union of two H-sets. We make precise this result in two directions, proving such a set may be, but need not be, a finite union of H-sets. Descriptive set theory tools like Cantor-Bendixson ranks are used; they are developed in the book of A. S. Kechris and A. Louveau [6]. Two proofs are presented; the first one is elementary while the second one is more general and useful. Using the last one I prove in my thesis,...
The following theorem is proved. Let f: X → Y be a finite-to-one map such that the restriction is an inductively perfect map for every countable compact set S ⊂ Y. Then Y is a countable union of closed subsets such that every restriction is an inductively perfect map.
The purpose of this note is to provide a substantial improvement and appreciable generalizations of recent results of Beg and Azam; Pathak, Kang and Cho; Shiau, Tan and Wong; Singh and Mishra.
We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.
In this paper, we prove some fixed point theorems for single valued mappings satisfying an implicit relation on space with two metrics. In addition we give a homotopy result using our theorems.
The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation....