Displaying similar documents to “On α -embedded sets and extension of mappings”

A semifilter approach to selection principles

Lubomyr Zdomsky (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal 𝔤 is a lower bound of the additivity number of the σ -ideal generated by Menger subspaces of the Baire space, and under 𝔲 < 𝔤 every subset X of the real line with the property Split ( Λ , Λ ) is Hurewicz, and thus it is consistent with ZFC that the property Split ( Λ , Λ ) is preserved by unions of less than 𝔟 subsets of the real line.

Pseudouniform topologies on C ( X ) given by ideals

Roberto Pichardo-Mendoza, Angel Tamariz-Mascarúa, Humberto Villegas-Rodríguez (2013)

Commentationes Mathematicae Universitatis Carolinae

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Given a Tychonoff space X , a base α for an ideal on X is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on α converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

Local extension of maps.

Barr, Michael, Kennison, John F., Raphael, R. (2009)

The New York Journal of Mathematics [electronic only]

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