Covering groups of nonconnected topological groups

All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in with pẽ = e there is a unique structure of topological group on such that ẽ is the identity and is a morphism of groups. We say that the structure of topological group on X lifts to .

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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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