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Displaying 41 – 60 of 363

A rigid space admitting compact operators

Paul Sisson (1995)

Studia Mathematica

A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid spaces was...

A Sequentially Compact Non-compact Quasi-pseudometric Space.

J. Ferrer, V. Gregori (1983)

Monatshefte für Mathematik

A solution to Comfort's question on the countable compactness of powers of a topological group

Artur Hideyuki Tomita (2005)

Fundamenta Mathematicae

In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number $α \leq 2^{}$ , a topological group G such that $G^{γ}$ is countably compact for all cardinals γ < α, but $G^{α}$ is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under $M A_{c o u n t a b l e}$ . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from $M A_{c o u n t a b l e}$ . However, the question has remained...

A theorem on mappings

Miroslav Katětov (1967)

Commentationes Mathematicae Universitatis Carolinae

A tiny peculiar Fréchet space

Roman Frič, Josef Novák (1984)

Czechoslovak Mathematical Journal

A topological characterization of stationary sets

Mohammad Ismail (1993)

Czechoslovak Mathematical Journal

A topological property of beta(N).

Nakassis, Anastase (1980)

International Journal of Mathematics and Mathematical Sciences

A tree $π$ -base for $ℝ^{*}$ without cofinal branches

Fernando Hernández-Hernández (2005)

Commentationes Mathematicae Universitatis Carolinae

We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree $π$ -base for $ℕ^{*}$ with no $ω_{2}$ branches yet of height $ω_{2}$ . We establish that this is also possible for $ℝ^{*}$ using a natural modification of Mathias forcing.

A Tychonoff non-normal space.

Tzannes, V. (1993)

International Journal of Mathematics and Mathematical Sciences

A uniquely homogeneous space need not be a topological group

Jan van Mill (1984)

Fundamenta Mathematicae

AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology

Horst Herrlich, Kyriakos Keremedis (2011)

Commentationes Mathematicae Universitatis Carolinae

We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.

Addition theorems, $D$ -spaces and dually discrete spaces

Ofelia Teresa Alas, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson (2009)

Commentationes Mathematicae Universitatis Carolinae

A neighbourhood assignment in a space $X$ is a family $𝒪 = {O_{x} : x \in X}$ of open subsets of $X$ such that $x \in O_{x}$ for any $x \in X$ . A set $Y \subseteq X$ is a kernel of $𝒪$ if $𝒪 (Y) = ⋃ {O_{x} : x \in Y} = X$ . If every neighbourhood assignment in $X$ has a closed and discrete (respectively, discrete) kernel, then $X$ is said to be a $D$ -space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf $P$ -space is a $D$ -space and we prove an addition...

Adequate families of sets and function spaces

Arkady G. Leiderman (1988)

Commentationes Mathematicae Universitatis Carolinae

Algebraic de Morgan's laws for non-commutative rings

Susan B. Niefield, Shu-Hao Sun (1995)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Algebras and spaces of dense constancies

Angelo Bella, Jorge Martinez, Scott D. Woodward (2001)

Czechoslovak Mathematical Journal

A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f \in C (X)$ there is a family of open sets ${U_{i} i \in I}$ , the union of which is dense in $X$ , such that $f$ , restricted to each $U_{i}$ , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean $f$ -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...

Algunas propiedades del ejemplo de Tychonoff de un espacio regular que no es completamente regular.

José Luis Blasco Olcina, Manuel López Pellicer (1974)

Collectanea Mathematica

Algunos resultados sobre anillos de Wallman.

José L. Blasco (1980)

Collectanea Mathematica

Almost maximal topologies on groups

Yevhen Zelenyuk (2016)

Fundamenta Mathematicae

Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...

An application of inaccessible alephs

Jan Chrastina (1977)

Archivum Mathematicum

An atriodic tree-like continuum with positive span which admits a monotone mapping to a chainable continuum

James Davis, W. Ingram (1988)

Fundamenta Mathematicae

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