Abstract
For every natural number n > 1, we construct a topological space X such that the clone segments of its Tychonoff modification TMX verify Clo k (X) = Clo k (T M X) if k < n and Clo n (X) is not isomorphic to Clo n (TMX).
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References
Cook, H.: Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241–249.
Herrlich, H.: On the concept of reflection in general topology, in: Contributions to Extension Theory of Topological Structures, Proc. Conf. Berlin, 1967, VEB Deutscher Verlag d. Wiss., Berlin, 1969, pp. 105–114.
Ishii, T.: On the Tychonoff functor and w-compactness, Topology Appl. 11 (1980), 173–187.
Oka, S.: Tychonoff functor and product spaces, Proc. Japan Acad. 54 (1978), 97–100.
Pupier, R.: La complétion universelle d’un produit d’espaces complètement réguliers, Publ. Dept. Math. Lyon 6 (1969), 75–84.
Sichler, J. and Trnkovâ, V.: Isomorphism and elementary equivalence of clone segments, Period. Math. Hungar. 32 (1996), 113–128.
Simon, P.: Completely regular modification and products, Comment. Math. Univ. Carolin. 25 (1) (1984), 121–128.
Taylor, W.: The clone of a topological space, in: Research and Exposition in Math. 13, Heldermann-Verlag, Berlin, 1986.
Trnkovâ, V.: Semirigid spaces, Trans. Amer. Math. Soc. 343 (1994), 305–325.
Trnkovâ, V.: Continuous and uniformly continuous maps of metric spaces, Topology Appl. 63 (1995), 189–200.
Trnkovâ, V.: Clone segments in Top and Unif, in: Categorical Topology, Proceedings of the L’Aquila Conference 1994, Kluwer Academic Publishers, Dordrecht, 1996, pp. 249–268.
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Dedicated to Bernhard Banaschewski on his 70th Birthday
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Tozzi, A., Trnková, V. (2000). Clone Segments of the Tychonoff Modification of Space. In: Brümmer, G., Gilmour, C. (eds) Papers in Honour of Bernhard Banaschewski. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2529-3_19
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DOI: https://doi.org/10.1007/978-94-017-2529-3_19
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