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...

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...

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...

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

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

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

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

and topological structures underlie the linear topological space (in other words, topological vector space) structure. A linear topological space is both...

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...

Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space is any...

fundamental group of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected...

and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms...

mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space ( X , τ ) {\displaystyle (X...

Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...

In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have...

of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient...

mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous...

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle...

In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. The Lindelöf property is a weakening of the...

claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...

In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition...

authors use the term topologically complete for a wider class of topological spaces, the completely uniformizable spaces. A topological space homeomorphic to...

motivates the definitions for general topological spaces. Take X, E and a as before, but now let X be a topological space. In this case, we replace metric...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time,...

normed vector space into a metric space and a topological vector space. If this metric space is complete then the normed space is a Banach space. Every normed...

topology and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair...

respectively, the topological boundary, interior, and closure of S {\displaystyle S} in X {\displaystyle X} . A topological space for which there exists...

of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important...

In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several...