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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Semirigid spaces

Author: Věra Trnková
Journal: Trans. Amer. Math. Soc. 343 (1994), 305-325
MSC: Primary 54B30; Secondary 08A40, 54B10, 54C05
MathSciNet review: 1219734
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Abstract: Semirigid spaces are introduced and used as a means to construct two metrizable spaces with isomorphic monoids of continuous self-maps and nonisomorphic clones; this resolves Problem 1 in [13]. The clone of any free variety of a given type with sufficiently many constants is shown to be isomorphic to the clone of a metrizable (semirigid) space.

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  • [1] Jiří Adámek and Věra Trnková, Automata and algebras in categories, Mathematics and its Applications (East European Series), vol. 37, Kluwer Academic Publishers Group, Dordrecht, 1990. MR 1071169
  • [2] Garrett Birkhoff and John D. Lipson, Heterogeneous algebras, J. Combinatorial Theory 8 (1970), 115–133. MR 0250887
  • [3] H. Cook, Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241–249. MR 0220249
  • [4] George Grätzer, Universal algebra, 2nd ed., Springer-Verlag, New York-Heidelberg, 1979. MR 538623
  • [5] J. de Groot, Groups represented by homeomorphism groups, Math. Ann. 138 (1959), 80–102. MR 0119193
  • [6] H. Herrlich, On the concept of reflection in general topology, Conf. on Contributions to Extension Theory of Topological Structures, Berlin, 1967.
  • [7] Horst Herrlich, Topologische Reflexionen und Coreflexionen, Lecture Notes in Mathematics, No. 78, Springer-Verlag, Berlin-New York, 1968 (German). MR 0256332
  • [8] C. Kuratowski, Topologie I, II, Monogr. Mat., Warsaw, 1950.
  • [9] F. William Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869–872. MR 0158921
  • [10] F. William Lawvere, Some algebraic problems in the context of functorial semantics of algebraic theories, Reports of the Midwest Category Seminar. II, Springer, Berlin, 1968, pp. 41–61. MR 0231882
  • [11] Aleš Pultr and Věra Trnková, Combinatorial, algebraic and topological representations of groups, semigroups and categories, North-Holland Mathematical Library, vol. 22, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 563525
  • [12] S. Świerczkowski, Topologies in free algebras, Proc. London Math. Soc. (3) 14 (1964), 566–576. MR 0161936
  • [13] W. Taylor, The clone of a topological space, Research and Exposition in Mathematics, vol. 13, Heldermann Verlag, Berlin, 1986. MR 879120
  • [14] Věra Trnková, Nonconstant continuous maps of spaces and of their 𝛽-compactifications, Topology Appl. 33 (1989), no. 1, 47–62. MR 1020982, 10.1016/0166-8641(89)90087-4
  • [15] V. Trnková and M. Hušek, Non-constant continuous maps of modifications of topological spaces, Comment. Math. Univ. Carolin. 29 (1988), 747-765.

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