In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric...

functional analysis. A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector...

Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous...

Hausdorff space. More generally, all metric spaces are Hausdorff. In fact, many spaces of use in analysis, such as topological groups and topological manifolds...

invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows...

is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X {\displaystyle X} is...

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous...

spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space"...

agree in a metric space, but may not be equivalent in other topological spaces. One such generalization is that a topological space is sequentially compact...

mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which has only...