Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods

Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

[EN] We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.This second author acknowledges the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals for funding this work through the projects IN151014 and IN141047.Choban, MM.; Berinde, V. (2017). Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance. Applied General Topology. 18(2):317-330. https://doi.org/10.4995/agt.2017.7067SWORD31733018

Spaces with sharp bases and with other special bases of countable order

AbstractWe study spaces with sharp bases and bases of countable order. A characterization of spaces with external bases of countable order is established (Theorem 2.7). Some necessary and sufficient conditions for a space X×S, where S is the convergent sequence, to have a sharp base are given (Theorem 3.2). It follows that a pseudocompact space X is metrizable iff X×S has a sharp base (Corollary 3.3). It is proved that a sharp base of finite rank is a uniform base (Theorem 4.4). Some other new results are also obtained, and some open questions are formulated

Selections, Paracompactness and Compactness

In the present paper, the Lindelof number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into complete metrizable (or discrete) spaces.Comment: 23 page

Efficiency and Penalty Factors on Monoids of Strings

In information theory, linguistics and computer science, metrics for measuring similarity between two given strings (sequences) are important. In this article we introduce efficiency, measure of similarity and penalty for given parallel decompositions of two strings. Relations between these characteristics are established. In this way, we continue the research from \cite{CB1, CB2}

Псевдокомпактни полу-топологични групи

Митрофан М. Чобан, Петър Ст. Кендеров, Уорън Б. Муурс - Полу-топологична група (съответно, топологична група) е група, снабдена с топология, относно която груповата оперция произведение е частично непрекъсната по всяка от променливите (съответно, непрекъсната по съвкупност от променливите и обратната операция е също непрекъсната). В настоящата работа ние даваме условия, от топологичен характер, една полу-топологична група да е всъщност топологична група. Например, ние показваме, че всяка сепарабелна псевдокомпактна полу-топологична група е топологична група. Показваме също, че всяка локално псевдокомпактна полу-топологична група, чиято групова операция е непрекъсната по съвкупност от променливите е топологична група.A semitopological group (topological group) is a group endowed with a topology for which multiplication is separately continuous (multiplication is jointly continuous and inversion is continuous). In this paper we give some topological conditions on a semitopological group that imply that it is a topological group. For example, we show that every separable pseudocompact group is a topological group. We also show that every locally pseudocompact group whose multiplication is jointly continuous is a topological group. *2010 Mathematics Subject Classification: Primary 22A10, 54E52, 54D30

Относно топологични групи и свойството на Бер в прираста

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Изследвани са прирасти със свойството на Бер на топологични групи.In this paper we study the remainders with Baire property of topological groups. ∗2000 Mathematics Subject Classification: 54A35, 63E35, 54D50.Partially supported by a contract of Sofia University of 2012