## Semirigid spaces

HTML articles powered by AMS MathViewer

- by Věra Trnková PDF
- Trans. Amer. Math. Soc.
**343**(1994), 305-325 Request permission

## 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.## References

- 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** - Garrett Birkhoff and John D. Lipson,
*Heterogeneous algebras*, J. Combinatorial Theory**8**(1970), 115–133. MR**250887**, DOI 10.1016/S0021-9800(70)80014-X - H. Cook,
*Continua which admit only the identity mapping onto non-degenerate subcontinua*, Fund. Math.**60**(1967), 241–249. MR**220249**, DOI 10.4064/fm-60-3-241-249 - George Grätzer,
*Universal algebra*, 2nd ed., Springer-Verlag, New York-Heidelberg, 1979. MR**538623** - J. de Groot,
*Groups represented by homeomorphism groups*, Math. Ann.**138**(1959), 80–102. MR**119193**, DOI 10.1007/BF01369667
H. Herrlich, - Horst Herrlich,
*Topologische Reflexionen und Coreflexionen*, Lecture Notes in Mathematics, No. 78, Springer-Verlag, Berlin-New York, 1968 (German). MR**0256332**, DOI 10.1007/BFb0074312
C. Kuratowski, - F. William Lawvere,
*Functorial semantics of algebraic theories*, Proc. Nat. Acad. Sci. U.S.A.**50**(1963), 869–872. MR**158921**, DOI 10.1073/pnas.50.5.869 - 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** - 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** - S. Świerczkowski,
*Topologies in free algebras*, Proc. London Math. Soc. (3)**14**(1964), 566–576. MR**161936**, DOI 10.1112/plms/s3-14.3.566 - W. Taylor,
*The clone of a topological space*, Research and Exposition in Mathematics, vol. 13, Heldermann Verlag, Berlin, 1986. MR**879120** - Věra Trnková,
*Nonconstant continuous maps of spaces and of their $\beta$-compactifications*, Topology Appl.**33**(1989), no. 1, 47–62. MR**1020982**, DOI 10.1016/0166-8641(89)90087-4
V. Trnková and M. Hušek,

*On the concept of reflection in general topology*, Conf. on Contributions to Extension Theory of Topological Structures, Berlin, 1967.

*Topologie*I, II, Monogr. Mat., Warsaw, 1950.

*Non-constant continuous maps of modifications of topological spaces*, Comment. Math. Univ. Carolin.

**29**(1988), 747-765.

## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**343**(1994), 305-325 - MSC: Primary 54B30; Secondary 08A40, 54B10, 54C05
- DOI: https://doi.org/10.1090/S0002-9947-1994-1219734-6
- MathSciNet review: 1219734