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Proceedings of the American Mathematical Society

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

 

 

Pseudocompact Whyburn spaces need not be Fréchet


Authors: Jan Pelant, Mihail G. Tkachenko, Vladimir V. Tkachuk and Richard G. Wilson
Journal: Proc. Amer. Math. Soc. 131 (2003), 3257-3265
MSC (2000): Primary 54A20, 54D99, 54F05, 54G10, 54G20
Published electronically: December 30, 2002
MathSciNet review: 1992867
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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 $\mathcal{P}$-space to be AP as well as a characterization of AP-property in linearly ordered topological spaces.


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Additional Information

Jan Pelant
Affiliation: Institute of Mathematics, Čech Academy of Sciences, Žitna 25, 11567, Prague, Čech 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: https://doi.org/10.1090/S0002-9939-02-06840-5
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
Published electronically: 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
Article copyright: © Copyright 2002 American Mathematical Society