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Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan — 1998

Serdica Mathematical Journal

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...

About Homogeneous Spaces and the Baire Property in Remainders Относно хомогенни пространства и свойството на Бер в прираста

Arhangel’skii, AlexanderChoban, MitrofanMihaylova, Ekaterina — 2012

Union of Bulgarian Mathematicians

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - В съобщението е продължено изследването на понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако co-хомогенното пространство X съдържа Gδ -гъсто Московско подпространство, тогава X е Московско пространство. In this paper we continue the study of the notions of o-homogeneous space, lo-homogeneous space, do-homogeneous space and co-homogeneous...

About Homogeneous Spaces and Conditions of Completeness of Spaces Относно хомогенни пространства и условия за пълнота

Arhangel’skii, AlexanderChoban, MitrofanMihaylova, Ekaterina — 2012

Union of Bulgarian Mathematicians

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Въведени са понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако lo-хомогенно пространство X има отворено подпространство, което е q-пълно, то и самото X е q-пълно. Показано е, че ако lo-хомогенно пространство X съдържа навсякъде гъсто екстремално несвързано подпространство, тогава X е екстремално несвързано. In this paper we introduce...

Pseudo-Compact Semi-Topological Groups Псевдокомпактни полу-топологични групи

Choban, MitrofanKenderov, PetarMoors, Warren — 2012

Union of Bulgarian Mathematicians

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...

About Topological Groups and the Baire Property in Remainders Относно топологични групи и свойството на Бер в прираста

Arhangel’skii, AlexanderChoban, MitrofanMihaylova, Ekaterina — 2012

Union of Bulgarian Mathematicians

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.

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