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Spaces

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Dynamic Topology

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

A topological space is a set X of elements together with a distinguished class of subsets called open sets satisfying the following axioms:

  1. (i)

    X and Ø are open sets;

  2. (ii)

    arbitrary unions of open sets are open;

  3. (iii)

    finite intersections of open sets are open.

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Bibliography

  • P. S. Alexandroff and Heinz Hopf, Topologie I, Berlin: Springer-Verlag, 1935.

    Google Scholar 

  • Maurice Fréchet, Les Espaces Abstraits, Paris: Monographies Borel, 1928.

    MATH  Google Scholar 

  • Felix Hausdorff, Gründzuge der Mengenlehre, Leipzig: Veit, 1914.

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  • Leopold Vietoris, Stetige Mengen, Monatshefte für Matematik und Physik, vol. 3 (1921), p. 173.

    Article  Google Scholar 

  • Heinrich Tietze, Beitrage zur allgemeinen Topologie I, Mathematische Annalen, vol. 88 (1923).

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  • Ernst Lindelöf, Sur quelques points de la théorie des ensembles, Comptes Rendus Hebdomadaires des Seances de L’Académie des Sciences, Paris, vol. 137 (1903).

    Google Scholar 

  • A. N. Tychonoff, Ãœber einen Metrizationsatz von P. Urysohn, Mathematische Annalen, vol. 95 (1926).

    Google Scholar 

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© 1979 Springer-Verlag New York Inc.

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Whyburn, G., Duda, E. (1979). Spaces. In: Dynamic Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6262-3_2

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  • DOI: https://doi.org/10.1007/978-1-4684-6262-3_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-6264-7

  • Online ISBN: 978-1-4684-6262-3

  • eBook Packages: Springer Book Archive

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