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Nonnormal spaces  with countable extent
Author(s):
Winfried
Just;
Ol'ga
V.
Sipacheva;
Paul
J.
Szeptycki
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1227-1235.
MSC (1991):
Primary 03E75, 54A20, 54A35, 54C35, 54G20
MathSciNet review:
1343704
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Abstract:
Examples of spaces  are constructed for which  is not normal but all closed discrete subsets are countable. A monolithic example is constructed in ZFC and a separable first countable example is constructed using  .
References:
- [A1]
- A.V. Arkhangel'skii, Topological Function Spaces, Mathematics and its Applications, 78, Kluwer Academic Publishers (1992). MR 92i:54022
- [A2]
- A.V. Arkhangel'skii,
 theory, In: Recent Progress in General Topology, Ed. M. Hu\v{s}ek and J. van Mill, North Holland (1992) 1-56. CMP 93:15 - [Ba]
- D.P. Baturov, On subspaces of function spaces, Vestn. Mosk. Univ. (1987) no, 4, 66-69; English transl. in Moscow Univ. Math. Bull. 42 (1987). MR 89a:54018
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 -products, Soviet Math. Dokl. 18 (1977) 1438-1442. MR 57:1395 - [K]
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 -products of metric spaces are normal, Preprint 1977.
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Additional Information:
Winfried
Just
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701
Email:
just@ace.cs.ohiou.edu
Ol'ga
V.
Sipacheva
Affiliation:
Chair of General Topology and Geometry, Mechanics and Mathematics Faculty, Moscow State University, 119899 Moscow, Russia
Email:
sipa@glas.apc.org
Paul
J.
Szeptycki
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701
Email:
szeptyck@ace.cs.ohiou.edu
DOI:
10.1090/S0002-9939-96-03500-9
PII:
S 0002-9939(96)03500-9
Keywords:
$C_{p}(X)$,
extent,
normality,
$\diamondsuit$,
almost disjoint family,
$\Psi$-space,
p-ultrafilter,
Luzin gap
Received by editor(s):
April 6, 1994
Additional Notes:
The first author was partially supported by NSF grant DMS-9312363.
The second author collaborated while visiting Ohio University.
Communicated by:
Franklin D. Tall
Copyright of article:
Copyright
1996,
American Mathematical Society
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