Search Results for ""

A manifold is said to be orientable if it can be given an orientation. Note the distinction between an "orientable manifold" and an "oriented manifold," where the former ...

An iterated fibration of Eilenberg-Mac lane spaces. Every topological space has this homotopy type.

A retraction is a continuous map of a space onto a subspace leaving each point of the subspace fixed. Alternatively, retraction can refer to withdrawal of a paper containing ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

A map phi:M->M where M is a manifold is C^r structurally stable if any C^r perturbation is topologically conjugate to phi. Here, C^r perturbation means a function psi such ...

The space join of a topological space X and a pair of points S^0, Sigma(X)=X*S^0.

The topological entropy of a map M is defined as h_T(M)=sup_({W_i})h(M,{W_i}), where {W_i} is a partition of a bounded region W containing a probability measure which is ...

Two maps phi,psi:M->M are said to be topologically conjugate if there exists a homeomorphism h:M->M such that phi degreesh=h degreespsi, i.e., h maps psi-orbits onto ...

A tubular neighborhood of a submanifold N in M is an embedding of the normal bundle (nu_N) of N into M, i.e., f:nu_N->M, where the image of the zero section of the normal ...