Search Results for ""

The limit points of a set P, denoted P^'.

One of the Eilenberg-Steenrod axioms. Let X be a single point space. H_n(X)=0 unless n=0, in which case H_0(X)=G where G are some groups. The H_0 are called the coefficients ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

A family of subsets of a topological space such that every point has a neighborhood that intersects only one of them.

A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the ...

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

A topology arising from a sheaf of continuous functions. It derives a natural topology from the projection operator. Etale spaces are examples of space that are not T2.

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M into disjoint pathwise-connected subsets. Then if F is a foliation of M, each F_alpha is called a leaf ...