Strongly homotopically stabile points

A. Lelek

Displaying similar documents to “Strongly homotopically stabile points”

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Yan-Kui Song (2015)

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A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.

Remarks on strongly star-Menger spaces

Yan-Kui Song (2013)

Commentationes Mathematicae Universitatis Carolinae

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A space $X$ is strongly star-Menger if for each sequence $(𝒰_{n} : n \in ℕ)$ of open covers of $X$ , there exists a sequence $(K_{n} : n \in N)$ of finite subsets of $X$ such that ${S t (K_{n}, 𝒰_{n}) : n \in ℕ}$ is an open cover of $X$ . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.

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We generalize a result of Choi and Effros on the range of a contractive completely positive projection in a C*-algebra to the case when this projection is only strongly positive using, moreover, an elementary argument instead of a 2×2-matrix technique.

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Hans Schoutens (1994)

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Quotients of Strongly Realcompact Groups

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A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the P-modification of topological groups and the operation of taking quotient groups.