Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T05:17:53.880Z Has data issue: false hasContentIssue false

A topological zero-one law for open continuous maps

Published online by Cambridge University Press:  17 April 2009

E. Barone
Affiliation:
Dipartimento di Matematica, via Arnesano, 73100 Lecce, Italy
K.P.S. Bhaskara Rao
Affiliation:
Indian Statistical Institute, Bangalore Centre, R.V. College Post, Bangalore 560 059, India Department of Mathematics, University of Brunei Darussalam, Bandar Sri Bepanian, Brunei
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain a topological zero-one law for sets with the Baire property which are invariant under a semigroup of open continuous maps acting on a topological space.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bhaskara Rao, M., and Bhaskara Rao, K.P.S., ‘A category analogue of the Hewitt-Savage zero-one law’, Proc. Amer. Math. Soc. 44 (1973), 497499.Google Scholar
[2]Bhaskara Rao, P.S. and Pol, R., ‘Topological zero-one laws’, Coll. Math. 39 (1978), 1323.CrossRefGoogle Scholar
[3]Kuratowski, K., ‘On the concept of strongly transitive systems in topology’, Ann. Mat. Pura Appl. 48 (1974), 357363.CrossRefGoogle Scholar
[4]Morgan, J.C. II, ‘On zero-one laws’, Proc. Amer. Math. Soc. 62 (1977), 353358.CrossRefGoogle Scholar
[5]Oxtoby, J.C., ‘Cartesian products of Baire spaces’, Fund. Math. 49 (1964), 157166.CrossRefGoogle Scholar
[6]Oxtoby, J.C., Measure and Category (Springer, Berlin, 1971).CrossRefGoogle Scholar