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Displaying similar documents to “Weak orderability of some spaces which admit a weak selection”

Lonely points revisited

Jonathan L. Verner (2013)

Commentationes Mathematicae Universitatis Carolinae

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In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point p ∈ X is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space 𝒢 ω from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745–748] to construct lonely points in ω * . This answers the question...

The regular topology on C ( X )

Wolf Iberkleid, Ramiro Lafuente-Rodriguez, Warren Wm. McGovern (2011)

Commentationes Mathematicae Universitatis Carolinae

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Hewitt [Rings of real-valued continuous functions. I., Trans. Amer. Math. Soc. 64 (1948), 45–99] defined the m -topology on C ( X ) , denoted C m ( X ) , and demonstrated that certain topological properties of X could be characterized by certain topological properties of C m ( X ) . For example, he showed that X is pseudocompact if and only if C m ( X ) is a metrizable space; in this case the m -topology is precisely the topology of uniform convergence. What is interesting with regards to the m -topology is that it is...

Weak selections and weak orderability of function spaces

Valentin Gutev (2010)

Czechoslovak Mathematical Journal

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It is proved that for a zero-dimensional space X , the function space C p ( X , 2 ) has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if X is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space E , the function space C p ( X , E ) is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides...