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Pseudocompact Whyburn spaces need not be Fréchet |
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| Authors: | Jan Pelant Mihail G Tkachenko Vladimir V Tkachuk Richard G Wilson |
| Institution: | Institute of Mathematics, Cech Academy of Sciences, Zitna 25, 11567, Prague, Cech Republic ; Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa, C.P. 09340, México D.F. ; Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina Iztapalapa, C.P. 09340, México D.F. ; Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina Iztapalapa, C.P. 09340, México D.F. |
| 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. |
| 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 |
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