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Not every near family is contained in a clan

Authors: S. A. Naimpally and J. H. M. Whitfield
Journal: Proc. Amer. Math. Soc. 47 (1975), 237-238
MSC: Primary 54E05
MathSciNet review: 0358703
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Abstract: In this note we solve an open problem concerning near structures and show that, unlike proximities and contiguities, not every near structure is induced by an elementary one.

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

  • [1] M. S. Gagrat and S. A. Naimpally, Proximity approach to extension problems, Fund. Math. 71 (1971), 63-76. MR 45 #2653. MR 0293576 (45:2653)
  • [2] M. S. Gagrat and W. J. Thron, Nearness and proximity extensions, Trans. Amer. Math. Soc. (to appear). MR 0385808 (52:6667)
  • [3] S. A. Naimpally, Reflective functors via nearness, Fund. Math. 85 (1974). MR 0353244 (50:5728)
  • [4] W. J. Thron, On a problem of F. Riesz concerning proximity structures, Proc. Amer. Math. Soc. 40 (1973), 323-326. MR 0322818 (48:1179)

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Keywords: Nearness, near structures, clan, proximity, contiguity
Article copyright: © Copyright 1975 American Mathematical Society

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