Article contents
Compactifications of semitopological semigroups II
Published online by Cambridge University Press: 09 April 2009
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.
Correcting some “proofs” given in an earlier paper of the same title, we prove here, among other things, that, if S is a subgroup of a topological group that is complete in a left invariant metric or locally compact, then every weakly almost periodic function on S is (left and right) uniformly continuous. We also prove a theorem related to results of R. B. Burckel and of W. W. Comfort and K. A. Ross: a topological group is pseudocompact if and only if WAP(G) = C(G).
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 129 - 134
- Copyright
- Copyright © Australian Mathematical Society 1976
References
Burckel, R. B. (1970), ‘Weakly Almost Periodic Functions on Semigroups’, Gordon and Breach, New York.Google Scholar
Burckel, R. B., ‘Mimeographed addendum to Weakly Almost Periodic Functions on Semigroups’.Google Scholar
Comfort, W. W. and Ross, K. A., (1966), ‘Pseudocompactness and uniform continuity in topological groups’, Pacific J. Math. 16, 483–496.CrossRefGoogle Scholar
Granirer, E. and Lau, A. T. (1971), ‘Invariant means on locally compact groups’, Illinois J. Math. 15, 249–257.Google Scholar
Grothendieck, A. (1952), ‘Critères de compacité dans les espaces fonctionnels généraux’, Amer. J. Math. 74, 168–186.Google Scholar
Katětov, M. (1951, 1953), ‘On real-valued functions in topological spaces’, Fund. Math. 38, 85–91, and correctionCrossRefGoogle Scholar
Macri, N. (1974), ‘The continuity of Arens product on the Stone-Čech compactification of semigroups’, Trans. Amer. Math. Soc. 191, 185–193.Google Scholar
Millnes, P. (1973), ‘Compactifications of semitopological semigroups’, J. Austral. Math. Soc. 15, 488–503.CrossRefGoogle Scholar
Mitchell, T. (1970), ‘Topological semigroups and fixed points’, Illinois J. Math. 14, 630–641.CrossRefGoogle Scholar
Rao, C. R. (1965), ‘Invariant means on spaces of continuous or measurable functions’, Trans. Amer. Math. Soc. 114, 187–196.Google Scholar
Weil, A. (1937), ‘Sur les espaces à structure uniforme et sur la topologie générale’, Hermann, Paris.Google Scholar
You have
Access
- 3
- Cited by