Adjective
homeomorphic (not comparable)
Having a homeomorphism
An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence : if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it. Source: Internet
For example, a Dehn filling with slope on any knot in the 3-sphere gives a homology sphere; typically these are not homeomorphic to the 3-sphere. Source: Internet
A torus is not homeomorphic to a sphere. Source: Internet
But the circle is not homeomorphic to the doughnut. Source: Internet
Elements of are sometimes called reals as well and though containing a homeomorphic image of in addition to being totally disconnected isn't even locally compact. Source: Internet
For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere? Source: Internet