topological space

In an arbitrary topological space this may not be possible.

In all of the following definitions, X is again a topological space.

More precisely, a topological space has a certain kind of set, called open sets.

For another example consider the category of topological spaces, Top.

In many examples the are not just sets but rather topological spaces.

The open sets of a topological space, ordered by inclusion.

This makes a topological space that is no longer a manifold.

Thus we use a category to generalize a topological space.

Some topological spaces may be endowed with a group law.

A topological space X is connected if these are the only two possibilities.

Any finite topological space, including the empty set, is compact.

A point is an element of a topological space.

As the above section on topological spaces makes clear, analysis isn't just about continuity in the traditional sense of real numbers.

Let G be a group and X a topological space.

There are stronger forms of connectedness for a topological space.

For each p this defines the same topological space.

The converse holds in many, but not all, topological spaces.

The word map means always a continuous function between topological spaces.

In mathematics, a branched surface is type of topological space.

A variety of topologies can be placed on a set to form a topological space.

This shows that the fundamental groups of any two topological spaces always have the same 'group structure'.

The word bounded makes no sense in a general topological space, without a metric.

This selection is subject to certain conditions: the axioms of a topological space.

Topological spaces show up naturally in almost every branch of mathematics.

To be more precise, let X be a topological space.