Hausdorff space

English Etymology en Felix Hausdorff 1868 1942 = German mathematician. Noun en topology A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that and . en 2005 N. L. Carothers A Short Course on Banach Space Theory https://books.google.com.au/books?id=pec4r3EsIiMC&pg=PA167&dq=%22Hausdorff+space%22%7C%22Hausdorff+spaces%22&hl=en&sa=X&ved=0ahUKEwi65vj2pcTWAhVIVLwKHcA0Ce0Q6AEIYDAL#v=onepage&q=%22Hausdorff%20space%22%7C%22Hausdorff%20spaces%22&f=false 167 w:Cambridge University Press More generally, each compact subset of a Hausdorff space is closed.Metric spaces and compact Hausdorff spaces enjoy an even stronger separation property; in either case, disjoint closed sets can always be separated by disjoint open sets. en 2008 Thiruvaiyaru V. Panchapagesan The Bartle-Dunford-Schwartz Integral Springer (Birkhäuser) https://books.google.com.au/books?id=bw7G5nTw7cUC&pg=PR9&dq=%22Hausdorff+space%22%7C%22Hausdorff+spaces%22&hl=en&sa=X&ved=0ahUKEwi65vj2pcTWAhVIVLwKHcA0Ce0Q6AEIlgEwFQ#v=onepage&q=%22Hausdorff%20space%22%7C%22Hausdorff%20spaces%22&f=false ix In 1953, Grothendieck [G] characterized locally convex Hausdorff spaces which have the Dunford-Pettis property and used this property to characterize weakly compact operators u : C(K) → F, where K is a compact Hausdorff space and F is a locally compact Hausdorff space (briefly, lcHs) which is complete. en 2012 Neil Hindman; Dona Strauss Algebra in the Stone-Cech Compactification: Theory and Applications 2nd https://books.google.com.au/books?id=mjmPHAhJkmYC&pg=PA83&dq=%22Hausdorff+space%22%7C%22Hausdorff+spaces%22&hl=en&sa=X&ved=0ahUKEwi65vj2pcTWAhVIVLwKHcA0Ce0Q6AEIjwEwFA#v=onepage&q=%22Hausdorff%20space%22%7C%22Hausdorff%20spaces%22&f=false 83 Walter de Gruyter Our construction of βD is a special case of more general constructions in which compact Hausdorff spaces are obtained using sets which are maximal subject to having certain algebraic properties. Synonyms topological space in which distinct points are contained in distinct open sets en T₂ space Hypernyms en sober space en topological space Hyponyms en metric space en normal space en regular space Translations Finnish: fi Hausdorffin avaruus German: de Hausdorff-Raum m Polish: pl przestrzeń Hausdorffa f en Topological spaces