Title: | On the quantification of uniform properties (English) |

Author: | Lowen, R. |

Author: | Windels, B. |

Language: | English |

Journal: | Commentationes Mathematicae Universitatis Carolinae |

ISSN: | 0010-2628 (print) |

ISSN: | 1213-7243 (online) |

Volume: | 38 |

Issue: | 4 |

Year: | 1997 |

Pages: | 749-759 |

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Category: | math |

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Summary: | Approach spaces ([4], [5]) turned out to be a natural setting for the quantification of topological properties. Thus a measure of compactness for approach spaces generalizing the well-known Kuratowski measure of non-compactness for metric spaces was defined ([3]). This article shows that approach uniformities (introduced in [6]) have the same advantage with respect to uniform concepts: they allow a nice quantification of uniform properties, such as total boundedness and completeness. (English) |

Keyword: | uniform space |

Keyword: | approach uniform space |

Keyword: | totally bounded |

Keyword: | precompact |

Keyword: | complete |

Keyword: | measure of total boundedness |

Keyword: | measure of completeness |

MSC: | 54B30 |

MSC: | 54E15 |

MSC: | 54E35 |

idZBL: | Zbl 0980.54020 |

idMR: | MR1603710 |

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Date available: | 2009-01-08T18:37:44Z |

Last updated: | 2012-04-30 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/118970 |

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Reference: | [1] Čech E.: Topological Spaces.Interscience Publishers, 1966. MR 0211373 |

Reference: | [2] Kuratowski C.: Sur les espaces complets.Fund. Math. 15 (1930), 301-309. |

Reference: | [3] Lowen R.: Kuratowski's measure of non-compactness revisited.Quarterly J. Math. Oxford 39 (1988), 235-254. Zbl 0672.54025, MR 0947504 |

Reference: | [4] Lowen R.: Approach spaces: a common supercategory of TOP and MET.Math. Nachrichten 141 (1989), 183-226. Zbl 0676.54012, MR 1014427 |

Reference: | [5] Lowen R.: Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad.Oxford Mathematical Monographs, Oxford University Press, 1997. Zbl 0891.54001, MR 1472024 |

Reference: | [6] Lowen R., Windels B.: AUnif, a common supercategory of pMET and Unif.to appear in Int. J. Math. Math. Sci. Zbl 0890.54024, MR 1486952 |

Reference: | [7] Lowen R., Windels B.: Quantifying completion.submitted for publication. Zbl 0962.54023 |

Reference: | [8] Preuss G.: Theory of Topological Structures.Kluwer Academic Publishers, 1987. Zbl 0649.54001, MR 0937052 |

Reference: | [9] Willard S.: General Topology.Addison Wesley Publishing Company, 1970. Zbl 1052.54001, MR 0264581 |

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