See the article on topological properties for more details and examples.

He was particularly interested in what topological properties characterized a sphere.

The language of covers is often used to define several topological properties related to compactness.

This article is (mostly) concerned with uniform properties that are not topological properties.

According to the designer's needs and the topological properties of the given network, several different weighting methods have been proposed.

This changes the topological properties of the surface and using the tube we can connect the three cottages without crossing lines.

Informally, a topological property is a property of the space that can be expressed using open sets.

Paracompact manifolds have all the topological properties of metric spaces.

Other surfaces may also be used, with their topological properties determining the degeneracy of the stabilizer space.

Two homeomorphic spaces share the same topological properties.

Cardinal functions are widely used in topology as a tool for describing various topological properties.

One important aspect is that these may have simpler topological properties: see for example Kuiper's theorem.

Using the Scott topological definition of open it is apparent that all topological properties are met.

A pseudoline arrangement is a family of curves that share similar topological properties with a line arrangement.

An illuminating example of the connections between game-theoretic notions and topological properties is the Sierpiński game.

To prove that two spaces are not homeomorphic it is sufficient to find a topological property not shared by them.

The topological property of having a base consisting of clopen sets is sometimes known as "zero-dimensionality".

Poincaré discovered that the answer can be found in what we now call the topological properties in the area containing the trajectory.

For some graphs, such as Delaunay triangulations, both metric and topological properties are of importance.

It preserves basic topological properties of the continuous equations such as conservation of charge and energy.

The study of topological properties of the fractional Hall effect remains an active field of research.

Instead of the topological properties of the domain, this theorem uses the fact that the function in question is a contraction.

If two spaces are homeomorphic, they have identical topological properties, and are considered topologically the same.

The topological properties of circular DNA are complex, and only a brief introduction can be presented here.

These spaces are quasi-compact, quasi-separated, and functorial in the rigid space, but lack a lot of nice topological properties.