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, topological space, space, spaces, topological spaces":
... 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 ... equivalently the set 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 ...
... functions are widely used in topology as a tool for describing various topological properties ... side of the definitions, 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 ... 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 ...
... 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 ...
Famous quotes containing the word space:
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (18171862)