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Topological space - Classification of topological spaces | | Topological space - Classification of topological spaces: Encyclopedia II - Topological space - Classification of topological spaces | | Topological spaces can be broadly classified, up to homeomorphism, by their topological properties. A topological property is a property of spaces that is invariant under homeomorphisms. To prove that two spaces are not homeomorphic it is sufficient to find a topological property which is not shared by them. Examples of such properties include connectedness, compactness, and various separation axioms.
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See also:Topological space, Topological space - Definition, Topological space - Comparison of topologies, Topological space - Continuous functions, Topological space - Alternative definitions, Topological space - Examples of topological spaces, Topological space - Topological constructions, Topological space - Classification of topological spaces, Topological space - Topological spaces with algebraic structure, Topological space - Topological spaces with order structure | | | Topological space, Topological space - Alternative definitions, Topological space - Classification of topological spaces, Topological space - Comparison of topologies, Topological space - Continuous functions, Topological space - Definition, Topological space - Examples of topological spaces, Topological space - Topological constructions, Topological space - Topological spaces with algebraic structure, Topological space - Topological spaces with order structure | | |
| | | Topological space: Encyclopedia II - Topological space - Classification of topological spaces
Topological space - Classification of topological spaces
Topological spaces can be broadly classified, up to homeomorphism, by their topological properties. A topological property is a property of spaces that is invariant under homeomorphisms. To prove that two spaces are not homeomorphic it is sufficient to find a topological property which is not shared by them. Examples of such properties include connectedness, compactness, and various separation axioms.
See the article on topological properties for more details and examples.
Other related archivesspecialization (or canonical) preorder, coarser, finer, Euclidean spaces, Hochster, K-theory, Kuratowski closure axioms, Polytope, Sierpinski space, T1, Topology, Vietoris, Zariski topology, accumulation points, algebraic objects, algebraic variety, axioms, balls, base, bijection, c, categories, category, category of topological spaces, closed sets, cofinite topology, compactness, complements, complete lattice, computational geometry, connectedness, continuous, convex, de Morgan's laws, discrete topology, empty set, equivalence classes, equivalence relation, function, functional analysis, generated, graphs, homeomorphism, homology theory, homotopy theory, if and only if, induction, intersection, intervals, invariants, inverse, inverse image, join, local field, local fields, lower limit topology, manifold, mathematics, meet, metric space, morphisms, neighbourhood, net, normed vector space, objects, open sets, operator, operators, ordinal, polynomial, power set, product topology, quotient space, real numbers, separation axioms, sequence, set, simplex, simplicial complex, spectral, spectrum of a ring, subsets, subspace topology, surjective, topological groups, topological properties, topological rings, topological vector spaces, topology, trivial topology, union, up to
 Adapted from the Wikipedia article "Classification of topological spaces", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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