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Factorizations of normality via generalizations of β -normality

Ananga Kumar Das, Pratibha Bhat, Ria Gupta (2016)

Mathematica Bohemica

The notion of β -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost β -normal spaces, which is a simultaneous generalization of β -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak β -normality, in terms of θ -closed sets, which turns out to be a simultaneous generalization of β -normality and θ -normality. A space X is said to be weakly β -normal (w β -normal ) if for every pair of disjoint...

Fiber orders and compact spaces of uncountable weight

Antonio Avilés, Ondřej F. K. Kalenda (2009)

Fundamenta Mathematicae

We study an order relation on the fibers of a continuous map and its application to the study of the structure of compact spaces of uncountable weight.

First countable spaces without point-countable π-bases

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2007)

Fundamenta Mathematicae

We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a first countable,...

Forcing tightness in products of fans

Jörg Brendle, Tim La Berge (1996)

Fundamenta Mathematicae

We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.

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