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Lattice-invariant properties of topological spaces


Author: Yim-ming Wong
Journal: Proc. Amer. Math. Soc. 26 (1970), 206-208
MSC: Primary 54.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0261549-9
MathSciNet review: 0261549
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Abstract: W. J. Thron proved in 1962 that regularity and normality are lattice-invariant properties but not $ {T_0}$
iexcl and $ {T_1}$. In the present paper it is proved that complete regularity, compactness, local compactness, Lindelöf, second countability and connectedness are lattice-invariant properties. It is also proved that Hausdorff, complete normality, separability, and first countability are not lattice-invariant properties.


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

  • [1] W. J. Thron, Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671-679. MR 26 #4307. MR 0146787 (26:4307)
  • [2] E. F. Steiner, Normal families and completely regular spaces, Duke Math. J. 33 (1966), 743-745. MR 33 #7975. MR 0199835 (33:7975)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0261549-9
Keywords: Lattice-invariant property, complete regularity, compactness, local compactness, Lindelöf, second countability, connectedness, Hausdorff, complete normality, separability, first countability
Article copyright: © Copyright 1970 American Mathematical Society

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