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
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References
S.P. Franklin and M. Rajagopalan, Some examples in Topology, Trans. Amer.Math. Soc. 155 (1971) 305–314
H. Herrlich and G.E. Stracker, Tòpologische Reflectionen and Coreflectionen, Springer Verlag Lecture Notes in Math. 78 (1969).
V. Kannan, Coreflexive Subcategories in Topology, Ph.D. Thesis, Madurai University (1970).
V. Kannan, Lattices of Topologies, Topology Seminar at Meerut (1977).
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
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