All Universal Coverings Are Spanier Spaces

Details All Universal Coverings Are Spanier Spaces All Universal Coverings Are Spanier Spaces

2011-11-29

arxiv.org/abs/1111.6736v1

Mathematics

Algebraic Topology

8 pages

Scientific paper

In this paper, we study necessary and sufficient conditions for existence of categorical universal coverings using open covers of a given space $X$. In fact, we define several homotopy theoretic conditions which we then prove are equivalent to the existence of a categorical universal covering space. As an application, we show that all universal coverings of a connected and locally path connected space are Spanier spaces.

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