Topology Proceedings 30 No. 1 (2006), pp. 379-388

Reflection Theorems for Some Cardinal Functions in Initially k-Compact Spaces

Alejandro Ramírez-Páramo

We establish that, in an initially k-compact T₃-space X, the property of having character at most k is discretely reflective; i.e., if X is initially k-compact, T₃, and c([`D]) ≤ k for any discrete D ⊂ X, then c(X) ≤ k. This generalizes an analogous result of Ofelia T. Alas, Vladimir V. Tkachuk, and Richard G. Wilson in [Closures of discrete sets often reflect global properties, Topology Proc. 25 (2000), Spring, 27-44] proved for compact spaces. We also extend over the class of initially k-compact T₃-spaces a result of Alan Dow in [An Introduction to Applications of Elementary Submodels to Topology, Topology Proc. 13, 1988, no. 1, 17-72] on reflecting uncountable character in countably compact spaces. Some corollaries on reflection of other cardinal functions are obtained.

Keywords: cardinal function, initially k-compact, reflection

Mathematics Subject Classification: 54A25 (54A35)

Document formats: PDF file 186.8 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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