-
given space. Two
spaces with a
homeomorphism between them are
called homeomorphic, and from a
topological viewpoint they are the same. Very
roughly speaking...
-
manifold which is closed, connected, and has
trivial fundamental group is
homeomorphic to the three-dimensional sphere.
Familiar shapes, such as the surface...
- any
arrangement of
bridges homeomorphic to
those in Königsberg, and the
hairy ball
theorem applies to any
space homeomorphic to a sphere. Intuitively,...
-
areas of mathematics, a
metrizable space is a
topological space that is
homeomorphic to a
metric space. That is, a
topological space ( X , τ ) {\displaystyle...
- In the
mathematical field of
topology a
uniform isomorphism or
uniform homeomorphism is a
special isomorphism between uniform spaces that
respects uniform...
- {\displaystyle X} is
locally homeomorphic to Y {\displaystyle Y} if
every point of X {\displaystyle X} has a
neighborhood that is
homeomorphic to an open subset...
-
Cantor space is a
topological space 2 N {\displaystyle 2^{\mathbb {N} }}
homeomorphic to the
Cantor set.[citation needed]
Binary is a
number system with a...
-
single equivalence class. Then I 2 / ∼ {\displaystyle I^{2}/\sim } is
homeomorphic to the
sphere S 2 . {\displaystyle S^{2}.}
Adjunction space. More generally...
- theory, two
graphs G {\displaystyle G} and G ′ {\displaystyle G'} are
homeomorphic if
there is a
graph isomorphism from some
subdivision of G {\displaystyle...
- three-dimensional
topological manifold which is
closed and simply-connected must be
homeomorphic to the 3-sphere.
Although the
conjecture is
usually stated in this form...
