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 | References | Similar Articles | Additional Information
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.
- W. J. Thron, Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671–679. MR 146787
- E. F. Steiner, Normal families and completely regular spaces, Duke Math. J. 33 (1966), 743–745. MR 199835
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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