A Class of Compact Rigid 0-Dimensional Spaces
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 817-821
Voir la notice de l'article provenant de la source Cambridge University Press
A topological space is called “rigid” if its autohomeomorphism group is trivial. In (1), de Groot and McDowell showed that there are rigid, 0- dimensional spaces of arbitrarily high cardinality but left open the question of whether or not there are compact,rigid, 0-dimensional spaces of arbitrarily high cardinality, pointing out that an affirmative answer implies the existence of arbitrarily large Boolean rings with trivial automorphism groups. In this paper we construct a class of rigid, 0-dimensional spaces X α of arbitrary infinite cardinality and show that their Stone-Cech compactifications βX α are also rigid, thus answering the above question affirmatively.I would like to thank S. W. Willard, J. R. Isbell, and the referee for their careful readings of preliminary versions of this paper.
Lozier, F. W. A Class of Compact Rigid 0-Dimensional Spaces. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 817-821. doi: 10.4153/CJM-1969-091-9
@article{10_4153_CJM_1969_091_9,
author = {Lozier, F. W.},
title = {A {Class} of {Compact} {Rigid} {0-Dimensional} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {817--821},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-091-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-091-9/}
}
[1] 1. de Groot, J. and McDowell, R. H., Autohomeomorphism groups of 0-dimensional spaces, Compositio Math. 15 (1963), 203–209. Google Scholar
[2] 2. Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, Princeton, N.J., 1960). Google Scholar
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