The connecting homomorphism is therefore a generalized winding number and measures the failure of " U " to be contractible.
42.
According to the Brouwer fixed-point theorem, every Kinoshita who found an example of a compact contractible space without the FPP.
43.
For finite dimensional " H ", this group would be a complex general linear group and not at all contractible.
44.
:* Every smooth homology sphere in dimension n \ geq 5 is homeomorphic to the boundary of a compact contractible smooth manifold.
45.
Persistent Betti numbers will be finite if X is a compact and locally contractible subspace of \ mathbb { R } ^ n.
46.
If the manifold is ?-compact and not compact the full diffeomorphism group is not locally contractible for any of the two topologies.
47.
Therefore any space can be embedded in a contractible one ( which also illustrates that subspaces of contractible spaces need not be contractible ).
48.
Therefore any space can be embedded in a contractible one ( which also illustrates that subspaces of contractible spaces need not be contractible ).
49.
Therefore any space can be embedded in a contractible one ( which also illustrates that subspaces of contractible spaces need not be contractible ).
50.
Describe efficient algorithms for determining whether a given cycle is contractible in the Rips complex of any finite point set in the Euclidean plane.
