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- In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties. Relative to the set of all real numbers carrying the standard topology, the set K = {1/n | n is a positive integer} is not closed since it doesn't contain its (only) limit point 0. Relative to the K-topology however, the set K is automatically decreed to be closed by adding ‘more’ basis elements to the standard topology on R. Basically, the K-topology on R is strictly finer than the standard topology on R. It is mostly useful for counterexamples in basic topology. (en)
- En mathématiques, la K-topologie, ou topologie de Smirnov de la suite supprimée, est une topologie particulière sur l'ensemble ℝ des réels, plus fine que la topologie usuelle et pour laquelle l'ensemble K des inverses des entiers naturels non nuls est fermé (alors que pour la topologie usuelle, 0, qui n'appartient pas à K, est un point d'accumulation de K). D'autres propriétés remarquables de cet espace en font un contre-exemple utile en topologie générale. (fr)
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- 3646 (xsd:nonNegativeInteger)
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- In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties. Relative to the set of all real numbers carrying the standard topology, the set K = {1/n | n is a positive integer} is not closed since it doesn't contain its (only) limit point 0. Relative to the K-topology however, the set K is automatically decreed to be closed by adding ‘more’ basis elements to the standard topology on R. Basically, the K-topology on R is strictly finer than the standard topology on R. It is mostly useful for counterexamples in basic topology. (en)
- En mathématiques, la K-topologie, ou topologie de Smirnov de la suite supprimée, est une topologie particulière sur l'ensemble ℝ des réels, plus fine que la topologie usuelle et pour laquelle l'ensemble K des inverses des entiers naturels non nuls est fermé (alors que pour la topologie usuelle, 0, qui n'appartient pas à K, est un point d'accumulation de K). D'autres propriétés remarquables de cet espace en font un contre-exemple utile en topologie générale. (fr)
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- K-topologie (fr)
- K-topology (en)
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