topological manifold

Its coefficients are known in the case of topological manifolds.

It is common to place additional requirements on topological manifolds.

After a line, the circle is the simplest example of a topological manifold.

See the discussion of boundary in topological manifold for more details.

Lie groups: These are topological manifolds that also carry a compatible group structure.

In mathematics, 4-manifold is a 4-dimensional topological manifold.

It is a one-dimensional topological manifold, with boundary in the case of the closed ray.

Kervaire exhibited topological manifolds with no smooth structure at all.

As mentioned above, in dimensions smaller than 4, there is only one differential structure for each topological manifold.

There is an "essentially unique" smooth structure for any topological manifold of dimension smaller than 4.

A topological manifold of dimension not equal to 4 has a handlebody decomposition.

A detailed study of the category of topological manifolds.

In the remainder of this article a manifold will mean a topological manifold.

At the same time, they provide, also, an effective construction of the rational Pontrjagin classes on topological manifolds.

If M is already a topological manifold, we require that the new topology be identical to the existing one.

The complex projective space is a -dimensional topological manifold with .

In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.

In fact, the idea can be made to make sense on any topological manifold, even if there is no Lebesgue measure there.

On the other hand, smooth manifolds are more rigid than the topological manifolds.

An n-manifold will mean a topological manifold such that every point has a neighborhood homeomorphic to R.

The most famous counterexample is the long line, which is a nonparacompact topological manifold.

In dimension 3 and lower, every topological manifold admits an essentially unique PL structure.

In dimension at least 5 the existence of topological manifolds not homeomorphic to a simplicial complex was an open problem.

In that case every topological manifold has a topological invariant, its dimension.

For most applications a special kind of topological manifold, a differentiable manifold, is used.