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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...
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...
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...
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...
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.
2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30.
In the present paper the Lindelöf 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.
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