On the topological centre of the algebra <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="normal">LUC</mml:mi><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="script">G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>∗</mml:mo></mml:msup></mml:math> for general topological groups

W. Ruppert has studied, and given examples of, compact left topological groups for which the left translation flow(λG,G)is equicontinuous. Recently, we considered an analogous distal condition that applies to the groups of dynamical type; for these the topological centre is dense, so the translation flow is equicontinuous only in the trivial case whenGis topological. In the present paper, we continue this work, exhibiting new characterizations of equicontinuity and distality of(λG,G); we also discuss examples and study some related matters.

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SOME PROPERTIES OF G-SPACES ACTED WITH TOPOLOGICAL GROUPS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.7.56 ◽

2020 ◽

Vol 9 (7) ◽

pp. 4917-4922

Author(s):

S. Sivakumar ◽

D. Lohanayaki

Keyword(s):

Topological Groups

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Homomorphisms of topological groups that cannot be factorized by weight and dimension

Mathematical Notes ◽

10.1007/bf01158253 ◽

1987 ◽

Vol 41 (3) ◽

pp. 226-228

Author(s):

V. G. Pestov

Keyword(s):

Topological Groups

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CONTINUITY OF MEASURABLE HOMOMORPHISMS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972708000610 ◽

2008 ◽

Vol 78 (1) ◽

pp. 171-176 ◽

Cited By ~ 2

Author(s):

JANUSZ BRZDȨK

Keyword(s):

Topological Group ◽

Abelian Group ◽

Baire Property ◽

Topological Groups ◽

Locally Compact ◽

Compact Topological Group ◽

Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

Georgian Mathematical Journal ◽

10.1515/gmj.2003.209 ◽

2003 ◽

Vol 10 (2) ◽

pp. 209-222

Author(s):

I. Bakhia

Keyword(s):

Wide Class ◽

Sufficient Conditions ◽

Topological Spaces ◽

Topological Groups ◽

Compact Spaces ◽

Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

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