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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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.


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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