Displaying similar documents to “A note on topological properties of non-Hausdorff manifolds.”

The Definition of Topological Manifolds

Marco Riccardi (2011)

Formalized Mathematics

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This article introduces the definition of n-locally Euclidean topological spaces and topological manifolds [13].

Perturbations of isometries between C(K)-spaces

Yves Dutrieux, Nigel J. Kalton (2005)

Studia Mathematica

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We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L. ...

On the cardinality of n-Urysohn and n-Hausdorff spaces

Maddalena Bonanzinga, Maria Cuzzupé, Bruno Pansera (2014)

Open Mathematics

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Two variations of Arhangelskii’s inequality X ⩽ 2 χ ( X ) - L ( X ) for Hausdorff X [Arhangel’skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967–970 (in Russian)] given in [Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343] are extended to the classes with finite Urysohn number or finite Hausdorff number.