-barrelled spaces, -bornological spaces: Ad addendum
Stanislav Tomášek (1970)
Commentationes Mathematicae Universitatis Carolinae
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Stanislav Tomášek (1970)
Commentationes Mathematicae Universitatis Carolinae
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Miroslav Hušek (1992)
Commentationes Mathematicae Universitatis Carolinae
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The problem whether every topological space has a compactification such that every continuous mapping from into a compact space has a continuous extension from into is answered in the negative. For some spaces such compactifications exist.
Chrisostomos Petalas, Theodoros Vidalis (2004)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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It is well known that a function from a space into a space is continuous if and only if, for every set in the image of the closure of under is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets of .
A. Sharma, Z. Ziegler (1987)
Studia Mathematica
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Jorma Arhippainen, Jukka Kauppi (2009)
Studia Mathematica
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We study subalgebras of equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.
K. K. Dube (1974)
Matematički Vesnik
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Raushan Z. Buzyakova (2007)
Fundamenta Mathematicae
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We show that if an uncountable regular cardinal τ and τ + 1 embed in a topological group G as closed subspaces then G is not normal. We also prove that an uncountable regular cardinal cannot be embedded in a torsion free Abelian group that is hereditarily normal. These results are corollaries to our main results about ordinals in topological groups. To state the main results, let τ be an uncountable regular cardinal and G a T₁ topological group. We prove, among others, the following...
Saak Gabriyelyan, Jerzy Kąkol, Arkady Leiderman (2015)
Fundamenta Mathematicae
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A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, , such that whenever β ≤ α for all . The class of all metrizable topological groups is a proper subclass of the class of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group is metrizable, and hence G is strictly angelic. We deduce from...
Taras Banakh, Tadeusz Dobrowolski, Anatoliĭ Plichko
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This volume consists of three relatively independent articles devoted to the topological study of the so-called operator images and weak unit balls of Banach spaces. These articles are: “The topological classification of weak unit balls of Banach spaces” by T. Banakh, “The topological and Borel classification of operator images” by T. Banakh, T. Dobrowolski and A. Plichko, and “Operator images homeomorphic to ” by T. Banakh. The articles summarize investigations that has been done by...
V. Swaminathan (1977)
Matematički Vesnik
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