Every Cech-analytic Baire semitopological group is a topological group

Bouziad, Ahmed

doi:10.1090/s0002-9939-96-03384-9

Cited by 61 publications

(20 citation statements)

References 18 publications

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“…Quasicontinuous functions are selections of minimal usco and minimal cusco maps [7,[9][10][11][12]. They found applications in the study of topological groups [4,21,23], in the study of dynamical systems [5], in the study of extensions of densely defined continuous functions [17], etc. The quasicontinuity is also used in the study of CHART groups [22].…”

Section: Introductionmentioning

confidence: 99%

Quasicontinuous functions and the topology of uniform convergence on compacta

Holá

Holý

2021

Filomat

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Let X be a Hausdorff topological space, Q(X,R) be the space of all quasicontinuous functions on X with values in R and ?UC be the topology of uniform convergence on compacta. If X is hemicompact, then (Q(X,R), ?UC) is metrizable and thus many cardinal invariants, including weight, density and cellularity coincide on (Q(X,R), ?UC). We find further conditions on X under which these cardinal invariants coincide on (Q(X,R), ?UC) as well as characterizations of some cardinal invariants of (Q(X,R), ?UC). It is known that the weight of continuous functions (C(R,R), ?UC) is ?0. We will show that the weight of (Q(R,R), ?UC) is 2c.

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Section: Introductionmentioning

confidence: 99%

Quasicontinuous functions and the topology of uniform convergence on compacta

Holá

Holý

2021

Filomat

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“…In 1957, Ellis [7] showed that every locally compact semitopological group is a topological group. In [6], Bouziad proved that everyCech-complete semitopological group is a topological group. Later Kenderov et al [9] proved that a strongly Baire semitopological group is a topological group.…”

Section: Introductionmentioning

confidence: 99%

On -Unfavourable Spaces

Wang¹,

Zhang²

2020

Bull. Aust. Math. Soc.

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To study when a paratopological group becomes a topological group, Arhangel’skii et al. [‘Topological games and topologies on groups’, Math. Maced. 8 (2010), 1–19] introduced the class of $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$ -unfavourable spaces. We show that every $\unicode[STIX]{x1D707}$ -complete (or normal) $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$ -unfavourable semitopological group is a topological group. We prove that the product of a $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$ -unfavourable space and a strongly Fréchet $(\unicode[STIX]{x1D6FC},G_{\unicode[STIX]{x1D6F1}})$ -favourable space is $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$ -unfavourable. We also show that continuous closed irreducible mappings preserve the $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$ -unfavourableness in both directions.

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“…Following [12], a function f from X to Z is called quasi-continuous at x 0 if for neighborhoods U and W of x 0 and f (x 0 ), respectively, there exists a nonempty open set V ⊆ U such that f (V ) ⊆ W. The function f is called quasi-continuous if it is quasi-continuous at each point of X. The notion of quasi-continuity plays an important role in the proof that some semi-topological groups are actually topological groups (see, e.g., [4,5,21]) and in the proof of some generalizations of Michael's selection theorem [7]. The notion of quasi-continuity is frequently used for establishing the existence of points of joint continuity of two variables functions.…”

Section: Introductionmentioning

confidence: 99%

Points of Continuity of Quasi-Continuous Functions

Neghaban

Mirmostafaee

2020

Tatra Mountains Mathematical Publications

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We study points of joint continuity of multi-variable separately quasi-continuous functions which are continuous with respect to one variable. We will show that the assumption of complete regularity in the paper of V. Maslyuchenko et al in ”Tatra Mt. Math. Pub. 68, (2017), 47–58” can be removed in some situations. Moreover, we use a topological game argument to prove that the set of points of continuity of functions with closed graph into ωΔ-spaces is a Gδ subset of its domain provided that its domain is a W-space.

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Every Cech-analytic Baire semitopological group is a topological group

Abstract: Abstract. Among other things, we prove the assertion given in the title. This solves a problem of Pfister.

Cited by 61 publications

References 18 publications

Quasicontinuous functions and the topology of uniform convergence on compacta

Quasicontinuous functions and the topology of uniform convergence on compacta

On -Unfavourable Spaces

Points of Continuity of Quasi-Continuous Functions

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