# Semantic search

Connected not implies path-connected, Connected sum of compact manifolds is compact, Hurewicz theorem, N-sphere is (n-1)-connected, N-sphere is simply connected for n greater than 1, Path-connected and T1 with at least two points implies uncountable, Path-connected implies connected, Seifert-van Kampen theorem, Suspension of path-connected space is simply connected, Union of two simply connected open subsets with path-connected intersection is simply connected