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Lattice completion of the metrizable topologies
Published online by Cambridge University Press: 09 April 2009
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Several classes of topological spaces which are either the infimum or supremum of a family of metrizable topologies in the lattice of topologies were given by Anderson [1]. In this paper we investigate the completion of the set of metrizable topologies in four distinct convergence structure lattices on an infinite set. We also observe the influence on these completions of the question regarding the existence of nonnormal ultrafilters which Čech [3] asserted could be neither provednor disproved using present mathematical axiom systems.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 447 - 449
- Copyright
- Copyright © Australian Mathematical Society 1974
References
[1]Anderson, B. A., Topologies comparable to metric topologies, (Proceedings of the Arizona State University Conference on General Topology, Tempe, 1967).Google Scholar
[2]Carstens, A. M., ‘The Lattice of pretopologies on an infinite set’, Pac. J. Math. 29 (1969), 67–71.CrossRefGoogle Scholar
[4]Hearsey, B. V. and Kent, D. C., ‘Convergence structures’, Port. Math. (1972), 105–118.Google Scholar
[5]Kent, D. C., ‘Convergence function 5 and their related topologies’, Fund. Math. 54 (1964), 125–133.CrossRefGoogle Scholar
[7]Kent, D. C., ‘Decisive convergence spaces, Fréchet spaces and sequential spaces’, Rocky Mountain J. Math 1 (1971), 367–374.CrossRefGoogle Scholar
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