Welcome to Topospaces (The Topology Wiki). This is a pre-alpha stage topology wiki primarily managed by Vipul Naik, a Ph.D. student in Mathematics at the University of Chicago. We have over 400 articles including some material in basic point-set topology. It is part of a broader subject wikis initiative -- see the subject wikis reference guide for more details
Simple space (DEFINITION): A path-connected space whose fundamental group is Abelian and acts trivially on all the higher homotopy groups.
Regularity is not refining-preserved (FACT): Passing to a finer topology does not preserve the property of being a regular space.
Applying compactness (SURVEY ARTICLE): Explore how the fact that a topological space is compact can be put to good use.