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Connectedness in the scale of a uniform space

Published online by Cambridge University Press:  09 April 2009

G. C. Leslie  and
D. C. Kent
G. C. Leslie
Affiliation:
Idaho State UniversityPocatello, Idaho, USA
D. C. Kent
Affiliation:
Washington State UniversityPullman, Washington, USA
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Associated with each uniform space (S, U) there is a uniform lattice (P, V, ≦) called the scale of (S, U). The scale was first introduced by D. Bushaw (see [2] and [3]) for the purpose of studying stability in topological dynamics. Further properties of the scale were investigated in [4], and this paper pursues one of the research problems suggested in the latter paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 305 - 312
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Bushaw, D., ‘On Boundedness in Uniform Spaces’, Fund. Math. 56 (1965), 295–300.CrossRefGoogle Scholar
[2]Bushaw, D., ‘A Stability Criterion For General Systems’, Math. Systems Theory, 1 (1967), 79–88.CrossRefGoogle Scholar
[3]Bushaw, D., ‘The Scale of a Uniform Space’, Proc. of the International Symposium on Topology and its Applications, Hercegnovi, Yugoslavia, 08 25–31, 1968.Google Scholar
[4]Kent, D. C., ‘On the Scale of a Uniform Space’, Inventiones Math. 4 (1967), 159–164.CrossRefGoogle Scholar
[5]Mrówka, S. and Pervin, W. J., ‘On Uniform Connectedness’, Proc. Amer. Math. Soc. 15 (1964), 446–449.CrossRefGoogle Scholar