Welcome to Topospaces (The Topology Wiki). This is a pre-alpha stage topology wiki primarily managed by Vipul Naik, a Ph.D. 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.
Connected manifold implies homogeneous (FACT): There is a homeomorphism taking any point of a connected manifold to any other point.
Proving compactness (SURVEY ARTICLE): Ever thought of how to prove a topological space is compact? Read about it.