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On precompact (quasi-) uniform structures

Author: P. Th. Lambrinos
Journal: Proc. Amer. Math. Soc. 62 (1977), 365-366
MSC: Primary 54E15
MathSciNet review: 0428292
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Abstract: The following are shown:

(1) The subbasis theorem on precompactness does not hold even in uniform spaces.

(2) The supremum of (even finitely many) precompact quasi-uniform structures is not necessarily precompact.

(3) A compact quasi-uniform space is not necessarily totally bounded.

These results contradict corresponding assertions in the literature.

References [Enhancements On Off] (What's this?)

  • [1] S. Gaal, Point set topology, Academic Press, New York and London, 1964. MR 30 # 1484. MR 0171253 (30:1484)
  • [2] J. L. Kelley, General topology, Van Nostrand, Princeton, N.J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [3] M. G. Murdeshwar and S. A. Naimpally, Quasi-uniform topological spaces, Noordhoff, Groningen, 1966. MR 35 #2267. MR 0211386 (35:2267)
  • [4] M. G. Murdeshwar and K. K. Theckedath, Boundedness in a quasi-uniform space, Canad. Math. Bull. 13 (1970), 367-370. MR 42 #5222. MR 0270333 (42:5222)
  • [5] J. L. Sieber and W. J. Pervin, Completeness in quasi-uniform spaces, Math. Ann. 158 (1965), 79-81. MR 30 #2449. MR 0172229 (30:2449)

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Keywords: Precompact (quasi-) uniform structures
Article copyright: © Copyright 1977 American Mathematical Society

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