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Pseudocompact Whyburn spaces need not be Fréchet
Author(s):
Jan
Pelant;
Mihail
G.
Tkachenko;
Vladimir
V.
Tkachuk;
Richard
G.
Wilson
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3257-3265.
MSC (2000):
Primary 54A20, 54D99, 54F05, 54G10, 54G20
Posted:
December 30, 2002
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Abstract:
We prove in ZFC that there exists a Tychonoff pseudocompact scattered AP-space of uncountable tightness. We give some sufficient and necessary conditions for a  -space to be AP as well as a characterization of AP-property in linearly ordered topological spaces.
References:
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- A. Dow, M.G. Tkachenko, V.V.Tkachuk, R.G. Wilson, Topologies generated by discrete subspaces, Glasnik Matematicki, to appear.
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Additional Information:
Jan
Pelant
Affiliation:
Institute of Mathematics, Cech Academy of Sciences, Zitna 25, 11567, Prague, Cech Republic
Email:
pelant@math.cas.cz
Mihail
G.
Tkachenko
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa, C.P. 09340, México D.F.
Email:
mich@xanum.uam.mx
Vladimir
V.
Tkachuk
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina Iztapalapa, C.P. 09340, México D.F.
Email:
vova@xanum.uam.mx
Richard
G.
Wilson
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina Iztapalapa, C.P. 09340, México D.F.
Email:
rgw@xanum.uam.mx
DOI:
10.1090/S0002-9939-02-06840-5
PII:
S 0002-9939(02)06840-5
Keywords:
Whyburn space,
weakly Whyburn space,
AP-space,
WAP-space,
pseudocompact space,
countably compact space,
scattered space,
Lindel\"{o}f $\mathcal{P}$-space,
linearly ordered space
Received by editor(s):
November 30, 2001
Received by editor(s) in revised form:
April 18, 2002
Posted:
December 30, 2002
Additional Notes:
This research was supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) of México, grant 400200-5-28411E
The first author's research was supported by the grant GA CR 201/00/1466
Communicated by:
Alan Dow
Copyright of article:
Copyright
2002,
American Mathematical Society
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