𝑄-composable properties, semigroups and 𝐶𝑀-homomorphisms

Bednarek, A. R.; Magill, K. D.

doi:10.1090/S0002-9947-1972-0312448-1

$Q$-composable properties, semigroups and $\textrm {CM}$-homomorphisms
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by A. R. Bednarek and K. D. Magill

Trans. Amer. Math. Soc. 174 (1972), 383-398

DOI: https://doi.org/10.1090/S0002-9947-1972-0312448-1

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Abstract:

A certain type of topological property is investigated. To each such property and each topological space satisfying various conditions there is associated, in a natural way, a semigroup of relations. The nonconstant, union and symmetry preserving homomorphisms from one such semigroup into another are completely determined and this results in a topological version of the Clifford-Miller Theorem on endomorphisms of the full binary relation semigroup on a set.

References

A. H. Clifford and D. D. Miller, Union and symmetry preserving endomorphisms of the semigroup of all binary relations on a set, Czechoslovak Math. J. 20(95) (1970), 303–314. MR 262395
K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
Kenneth D. Magill Jr., Composable topological properties and semigroups of relations, J. Austral. Math. Soc. 11 (1970), 265–275. MR 0270319
K. D. Magill Jr. and S. Yamamuro, Union and symmetry preserving homomorphisms of semigroups of closed relations, Semigroup Forum 3 (1971/72), no. 2, 168–172. MR 291326, DOI 10.1007/BF02572957
K. D. Magill Jr. and S. Yamamuro, Union and symmetry preserving homomorphisms of semigroups of closed relations, Proc. London Math. Soc. (3) 24 (1972), 59–78. MR 291327, DOI 10.1112/plms/s3-24.1.59
D. B. McAlister, Homomorphisms of semigroups of binary relations, Semigroup Forum 3 (1971/72), no. 2, 185–188. MR 291328, DOI 10.1007/BF02572960