# Topological Space

Topological Space

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The branch of mathematics that studies topological spaces in their own right is called topology.

### Other articles related to "space, topological space, spaces, topological spaces, topological":

Locally Finite Collection - Examples and Properties - Compact Spaces
... No infinite collection of a compact space can be locally finite ... Indeed, let {Ga} be an infinite family of subsets of a space and suppose this collection is locally finite ... For each point x of this space, choose a neighbourhood Ux that intersects the collection {Ga} at only finitely many values of a ...
Topological Space - Specializations and Generalizations
... The following spaces and algebras are either more specialized or more general than the topological spaces discussed above ... Proximity spaces provide a notion of closeness of two sets ... Metric spaces embody a metric, a precise notion of distance between points ...
Cardinal Functions in Topology
... Cardinal functions are widely used in topology as a tool for describing various topological properties ... of the definitions, etc.) Perhaps the simplest cardinal invariants of a topological space X are its cardinality and the cardinality of its topology ... The weight w(X ) of a topological space X is the cardinality of the smallest base for X ...
Formal Scheme - Definition
... Let A be a (Noetherian) topological ring, that is, a ring A which is a topological space such that the operations of addition and multiplication are continuous ... of prime ideals of, is the underlying topological space of the formal spectrum of A, denoted Spf A ... All the spectra of have the same underlying topological space but a different structure sheaf ...
Collectionwise Normal Space
... In mathematics, a topological space is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ... Many authors assume that is also a T1 space as part of the definition, i ... A collectionwise normal T1 space is a collectionwise Hausdorff space ...

### Famous quotes containing the word space:

The secret ones around a stone
Their lips withdrawn in meet surprise
Lie still, being naught but bone
With naught but space within their eyes....
Allen Tate (1899–1979)