Ultra-b-barrelled spaces and the completeness of $L_{b}(E, F)$

Z. Kadelburg

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On topological groups with a small base and metrizability

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, $U_{α} : α \in ℕ^{ℕ}$ , such that $U_{α} \subset U_{β}$ whenever β ≤ α for all $α, β \in ℕ^{ℕ}$ . The class of all metrizable topological groups is a proper subclass of the class $T G_{}$ 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 $G \in T G_{}$ is metrizable, and hence G is strictly angelic. We deduce from...

A note on $R_{0}$ -topological spaces

K. K. Dube (1974)

Matematički Vesnik

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$M$ -barrelled spaces, $M$ -bornological spaces: Ad addendum

Stanislav Tomášek (1970)

Commentationes Mathematicae Universitatis Carolinae

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On the Hausdorff Dimension of Topological Subspaces

Tomasz Szarek, Maciej Ślęczka (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is shown that every Polish space X with $d i m_{T} X \geq d$ admits a compact subspace Y such that $d i m_{H} Y \geq d$ where $d i m_{T}$ and $d i m_{H}$ denote the topological and Hausdorff dimensions, respectively.

Linear topological properties of the Lumer-Smirnov class of the polydisc

Marek Nawrocki (1992)

Studia Mathematica

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Linear topological properties of the Lumer-Smirnov class $L N_{*} (^{n})$ of the unit polydisc $^{n}$ are studied. The topological dual and the Fréchet envelope are described. It is proved that $L N_{*} (^{n})$ has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for $L N_{*} (^{n})$ .

Remarks on flat and differential $K$ -theory

Man-Ho Ho (2014)

Annales mathématiques Blaise Pascal

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In this note we prove some results in flat and differential $K$ -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential $K$ -theory and Freed-Lott differential $K$ -theory.

$R_{0}$ and $R_{1}$ topological spaces

C. Dorsett (1978)

Matematički Vesnik

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On $R_{0}$ and $R_{1}$ topological spaces

D. Janković (1981)

Matematički Vesnik

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A note on $R_{0}$ and $R_{1}$ topological spaces

M. R. Žižović (1986)

Matematički Vesnik

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Nonnormality of remainders of some topological groups

Aleksander V. Arhangel&#039;skii, J. van Mill (2016)

Commentationes Mathematicae Universitatis Carolinae

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It is known that every remainder of a topological group is Lindelöf or pseudocompact. Motivated by this result, we study in this paper when a topological group $G$ has a normal remainder. In a previous paper we showed that under mild conditions on $G$ , the Continuum Hypothesis implies that if the Čech-Stone remainder $G^{*}$ of $G$ is normal, then it is Lindelöf. Here we continue this line of investigation, mainly for the case of precompact groups. We show that no pseudocompact group, whose weight...

Remarks on $\mathcal{S}$ -Closedness in Topological Spaces

Zbigniew Duszyński (2007)

Bollettino dell'Unione Matematica Italiana

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Corresponding to [27], some properties of S-closed subspaces and subsets $\mathcal{S}$ -closed relative to a topological space are proved. Conditions under which mappings preserve certain $\mathcal{S}$ -closed subspaces are investigated.

Displaying similar documents to “Ultra-b-barrelled spaces and the completeness of L b ( E , F ) ”

Displaying similar documents to “Ultra-b-barrelled spaces and the completeness of $L_{b} (E, F)$ ”