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Título del libro: Open Problems In Topology Ii
Título del capítulo: Tightness and T-Equivalence

Autores UNAM:
OLEG OKOUNEV;
Autores externos:
Idioma:
Inglés
Año de publicación:
2007
Resumen:

This chapter provides an overview of tightness and t-equivalence. Two spaces X and Y are called M-equivalent if their free topological groups F(X) and F(Y) in the sense of Markov are topologically isomorphic. The spaces X and Y are l-equivalent if the spaces Cp(X) and Cp(Y) of real-valued continuous functions equipped with the topology of point-wise convergence are linearly homeomorphic, and t-equivalent if Cp(X) and Cp(Y) are homeomorphic; Arhangel'ski? has shown that M-equivalence of two spaces implies their l-equivalence; clearly, l-equivalent spaces are t-equivalent. A topological property is preserved by an equivalence relation if whenever two spaces are in the relation, one of them has the property if and only if the other one does. Similarly, a cardinal invariant is preserved by a relation if its values on two spaces are the same whenever the spaces are in the relation. The chapter discusses about the example that shows the non-preservation of the tightness by M-equivalence depends heavily on the fact that one of the two spaces is not normal. The chapter also discuses problems based on M-equivalent Lindelof spaces. © 2007 Elsevier B.V. All rights reserved.

Entidades citadas de la UNAM:
Fuente:


ISBN:
9780444522085
Editorial:
Elsevier Nombre de la publicación:
Tightness and T-Equivalence
Página inicial:
581
Página final:
584

Tipo de producto:
Capítulo de un Libro



DOI:
10.1016/B978-044452208-5/50053-3