Results 51 to 60 of about 116 (108)
F-points in countably compact spaces
Applied General Topology, 2001 Answering a question of A.V. Arhangel'skii, we show that any extremally disconnected subspace of a compact space with countable tightness is discrete.
Angelo Bella, V.I. Malykhin
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Pseudocompactness of hyperspaces
Topology and its Applications, 2007 Pour tout espace \(X\), soit \(2^X\) l'espace des fermés non vides de \(X\) muni de la topologie de Vietoris. Les auteurs étudient la question de savoir si la pseudocompacité du produit dénombrable \(X^\omega\) entraîne la pseudocompacité de \(2^X\), et construisent un exemple montrant que ce n'est pas toujours le cas. Ils considèrent en particulier le
Hrušák, Michael +2 more
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An operation on topological spaces
Applied General Topology, 2000 A (binary) product operation on a topological space X is considered. The only restrictions are that some element e of X is a left and a right identity with respect to this multiplication, and that certain natural continuity requirements are satisfied ...
A.V. Arhangelskii
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Applied General Topology, 2008 In this note a new class of topological spaces generalizing k-spaces, the pseudo-k-spaces, is introduced and investigated. Particular attention is given to the study of products of such spaces, in analogy to what is already known about k-spaces and quasi-
Anna Maria Miranda
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Ascoli’s theorem for pseudocompact spaces [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020 A Tychonoff space $X$ is called ({\em sequentially}) {\em Ascoli} if every compact subset (resp. convergent sequence) of $C_k(X)$ is equicontinuous, where $C_k(X)$ denotes the space of all real-valued continuous functions on $X$ endowed with the compact-open topology. The classical Ascoli theorem states that each compact space is Ascoli. We show that a
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Topology and its Applications, 1998 The paper is full of interesting results on pseudocompact spaces. The main result generalizes Comfort-Ross theorems [\textit{W. W. Comfort} and \textit{K. A. Ross}, Pac. J. Math. 16, 483-496 (1966; Zbl 0214.28502)]: (1) Every product of pseudocompact Mal'tsev spaces is pseudocompact; (2) If \(X\) is a pseudocompact Mal'tsev space, then every Mal'tsev ...
Reznichenko, E.A., Uspenskij, V.V.
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Topologies between compact and uniform convergence on function spaces
, 1991 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 1, Page 101-109, 1993.
S. Kundu, R. A. McCoy
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The character of free topological groups II
Applied General Topology, 2005 A systematic analysis is made of the character of the free and free abelian topological groups on metrizable spaces and compact spaces, and on certain other closely related spaces.
Peter Nickolas, Mikhail Tkachenko
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Set-open topologies on function spaces
Applied General Topology, 2018 Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and ...
Wafa Khalaf Alqurashi +2 more
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The partially pre-ordered set of compactifications of Cp(X, Y)
Topological Algebra and its Applications, 2015 In the set of compactifications of X we consider the partial pre-order defined by (W, h) ≤X (Z, g) if there is a continuous function f : Z ⇢ W, such that (f ∘ g)(x) = h(x) for every x ∈ X. Two elements (W, h) and (Z, g) of K(X) are equivalent, (W, h) ≡X (
Dorantes-Aldama A. +2 more
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