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Proceedings of the American Mathematical Society

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Characterizing topologies by functions


Author: Melvin C. Thornton
Journal: Proc. Amer. Math. Soc. 36 (1972), 613-614
MSC: Primary 54C40
DOI: https://doi.org/10.1090/S0002-9939-1972-0309055-9
MathSciNet review: 0309055
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Abstract: The multiplicative structure of the idempotents in the semiring of nonnegative lower semicontinuous functions on a large class of spaces determines the topology of the space.


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

  • [1] D. Drake and W. J. Thron, On the representations of an abstract lattice as the family of closed sets of a topological space, Trans. Amer. Math. Soc. 120 (1965), 57-71. MR 32 #6390. MR 0188963 (32:6390)
  • [2] R. Neilsen and C. Sloyer, Ideals of semi-continuous functions and compactifications of $ {T_1}$ spaces, Math. Ann. 187 (1970), 329-331. MR 42 #8450. MR 0273572 (42:8450)
  • [3] W. J. Thron, Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671-679. MR 26 #4307. MR 0146787 (26:4307)

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DOI: https://doi.org/10.1090/S0002-9939-1972-0309055-9
Keywords: Lattice of closed sets, semicontinuous functions
Article copyright: © Copyright 1972 American Mathematical Society

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