Topological fundamental groups and small generated coverings

Details Topological fundamental groups and small generated coverings Topological fundamental groups and small generated coverings

2011-02-05

arxiv.org/abs/1102.1080v1

Mathematics

Algebraic Topology

16 pages, 1 figure

Scientific paper

This paper is devoted to study some topological properties of the SG subgroup, $\pi_1^{sg}(X,x)$, of the topological fundamental group of a based space $(X,x)$, $\pi^{top}(X,x)$, and its influence on the existence of universal covering of $X$. First, we introduce small generated spaces which have indiscrete topological fundamental groups and also small generated coverings which are universal coverings in the categorical sense. Second, we give a necessary and sufficient condition for the existence of the small generated coverings. Finally, by introducing the notion semi-locally small generatedness, we show that the topological fundamental group of semi-locally small generated spaces are topological groups.

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