Example image of eyePlorer eyePlorer map for 'Contractible space': Homotopy Identity function Mathematics Topological space Homotopy group Trivial group Reduced homology Singular homology Deformation retract Cone (topology) Connected space If and only if Simply connected space N-connected Neighbourhood (mathematics) Neighbourhood system Locally connected space Locally simply connected space Euclidean space Star domain Whitehead manifold N-sphere Contractibility of unit sphere in Hilbert space Hilbert space Unit sphere House with two rooms Hawaiian earring CW complex Manifold Fake 4-ball Aspherical space Kuiper's theorem Weakly contractible Acyclic space Alexander duality Argument principle Classifying space Scherk–Schwarz mechanism Simply connected at infinity Dunce hat (topology) Equivariant cohomology Pseudocircle Solid torus Unit interval Nerve of a covering Cohomological dimension Exponential sheaf sequence Closed and exact differential forms Collapse (topology) Farrell–Jones conjecture