Paracompactness in countable products via the Souslin operation
Paracompactness in ordered spaces
Paracompactness in the class of closed images of GO-spaces
Paracompactness of topological completions
Paracompactness with respect to an ideal.
Partial discretization of topologies
In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.
Partition continue de l'unite et C-repletion.
P-embedding and product spaces
Perfect pre-images of cofinally complete metric spaces
We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.
Point-countable π-bases in first countable and similar spaces
It is a classical result of Shapirovsky that any compact space of countable tightness has a point-countable π-base. We look at general spaces with point-countable π-bases and prove, in particular, that, under the Continuum Hypothesis, any Lindelöf first countable space has a point-countable π-base. We also analyze when the function space has a point-countable π -base, giving a criterion for this in terms of the topology of X when l*(X) = ω. Dealing with point-countable π-bases makes it possible...
Preparacompactness and ℵ-preparacompactness in q-spaces
Preservation and reflection of properties acc and hacc
The aim of the paper is to study the preservation and the reflection of acc and hacc spaces under various kinds of mappings. In particular, we show that acc and hacc are not preserved by perfect mappings and that acc is not reflected by closed (nor perfect) mappings while hacc is reflected by perfect mappings.
Prime filters with CIP
Product properties for pairwise Lindelöf spaces.
Products of Lindelöf -spaces are Lindelöf – in some models of ZF
The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, • amusing that finite summability of the Lindelöf property takes place if either some weak choice principle...
Products of topological spaces and families of filters
We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by factors are Lindelöf. Parallel results are obtained for final -compactness, -compactness, the Menger and the Rothberger properties.
Projectivity of pure ideals
Property and dominating families
Generalizations of earlier negative results on Property are proved and two questions on an -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ is regular” and “” the existence of a separable locally compact -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants...
Property Q.
Pseudocompactness and the cozero part of a frame
A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a -frame and to Alexandroff spaces.