**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.

Read more about Topological Space: Definition, Comparison of Topologies, Continuous Functions, Examples of Topological Spaces, Topological Constructions, Classification of Topological Spaces, Topological Spaces With Algebraic Structure, Topological Spaces With Order Structure, Specializations and Generalizations

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

**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 ...

... are widely used in topology as a tool for describing various

**topological**properties ... etc.) Perhaps the simplest cardinal invariants of a

**topological space**X are its cardinality and the cardinality of its topology, denoted respectively by

... 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:

“In the tale proper—where there is no *space* for development of character or for great profusion and variety of incident—mere construction is, of course, far more imperatively demanded than in the novel.”

—Edgar Allan Poe (1809–1849)