contractible การใช้

• Spaces that are homotopy equivalent to a point are called contractible.
• Any fiber bundle over a contractible CW-complex is trivial.
• Since is a fibration with contractible fibre, sections of exist.
• Non-contractible in general have non-trivial de Rham cohomology.
• Furthermore, every cone is contractible to the vertex point by the homotopy
• For example, an open ball is a contractible manifold.
• All manifolds homeomorphic to the ball are contractible, too.
• In particular, the universal covering of such a space is contractible.
• Every collapsible complex is contractible, but the converse is not true.
• Since the half-plane is contractible, all bundle structures are trivial.
• The cone on a space " X " is always contractible.
• Every contractible space is path connected and simply connected.
• There exists a contractible space on which acts freely.
• If is contractible then and are homotopy equivalent spaces.
• In fact, these satisfy the much stronger property of being locally contractible.
• In particular, cv _ n is also contractible.
• It makes no sense at this point to talk about the most contractible issue.
• The first is that of homotopy contractible complexes.
• A square is a contractible topological space, which implies that it has trivial homology.
• This results were later generalized to other contractible manifolds by Casson, Harer and Stern.