connected space
topological space that cannot be written as the disjoint union of two nonempty open subsets
continuum
nonempty compact connected metric space in point-set topology
topologist's sine curve
connected but not path-connected space; the graph of the function sin(1/𝑥) on the half-open interval (0,1] together with the origin
unitary group
group of unitary matrices
connected component
topological space
domain
connected open subset of a finite-dimensional vector space
special orthogonal group
connected component of O(n) containing the identity
path-connected space
topological space such that any two points can be connected by a path
homology sphere
topological manifold whose homology coincides with that of a sphere, i.e. trivial except in the top and bottom degrees, where it has a single generator