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Pairs of topologies with same family of continuous self-maps

Part of the Lecture Notes in Mathematics book series (LNM,volume 719)

Abstract

We characterize pairs of comparable topologies with same family of continuous self-maps, in terms of categorical notions. This requires a description of bireflection in the bireflective hull of a given family of topological spaces; this is obtained in the first section. The known characterizations of bireflective subcategories of TOP follow as easy consequences of this description of bireflection.

Keywords

  • Topological Space
  • Weak Topology
  • Finite Product
  • Unique Topology
  • Coreflective Subcategory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. S.P. Franklin and M. Rajagopalan, Some examples in Topology, Trans. Amer.Math. Soc. 155 (1971) 305–314

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  3. V. Kannan, Coreflexive Subcategories in Topology, Ph.D. Thesis, Madurai University (1970).

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  4. V. Kannan, Lattices of Topologies, Topology Seminar at Meerut (1977).

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  5. J.F. Kenison, Reflective functors in General Topology and elsewhere, Trans.Amer.Math.Soc.(1965)118,303–315.

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© 1979 Springer-Verlag

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Kannan, V. (1979). Pairs of topologies with same family of continuous self-maps. In: Herrlich, H., Preuß, G. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065270

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  • DOI: https://doi.org/10.1007/BFb0065270

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09503-3

  • Online ISBN: 978-3-540-35193-1

  • eBook Packages: Springer Book Archive