{\displaystyle X} and Y {\displaystyle Y} are homeomorphic. A self-homeomorphism is a homeomorphism from a topological space onto itself. Being "homeomorphic"...

mathematics, particularly topology, the homeomorphism group of a topological space is the group consisting of all homeomorphisms from the space to itself with function...

group elements are assumed to act as homeomorphisms on X. The structure of a G-space is a group homomorphism ρ : G → Homeo(X) into the homeomorphism group...

automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism (see homeomorphism group). In this example it is not sufficient...

fundamental group); all homotopy equivalences of the torus can be realized by homeomorphisms – every homotopy equivalence is homotopic to a homeomorphism. Thus...

spaces, Top. Representations in Top are homomorphisms from G to the homeomorphism group of a topological space X. Two types of representations closely related...

isomorphism Euclidean plane isometry Flat (geometry) Homeomorphism group Involution Isometry group Motion (geometry) Myers–Steenrod theorem 3D isometries...

isomorphism that is also a homeomorphism of the underlying topological spaces. This is stronger than simply requiring a continuous group isomorphism—the inverse...

The precise locations of the holes are irrelevant, because the homeomorphism group acts k-transitively on any connected manifold of dimension at least...

space G \ X. Now assume G is a topological group and X a topological space on which it acts by homeomorphisms. The action is said to be continuous if the...