Products of locally connected locales
Products of normal spaces with Lašnev spaces
Products of perfectly normal spaces
Products of quotients and of -spaces
Products of sequential convergence properties
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.
Products of topological spaces represent any semigroup (Preliminary communication)
Produit topologique, produit tensoriel et -replétion
Projective potencies and multiplicative extension operators
Projectively generated convergence of sequences
Projectivity of pure ideals
Proper shape retracts
Properties of a pair of functions which generate a dense subsemigroup of S(X).
Properties of one-point completions of a noncompact metrizable space
If a metrizable space is dense in a metrizable space , then is called a metric extension of . If and are metric extensions of and there is a continuous map of into keeping pointwise fixed, we write . If is noncompact and metrizable, then denotes the set of metric extensions of , where and are identified if and , i.e., if there is a homeomorphism of onto keeping pointwise fixed. is a large complicated poset studied extensively by V. Bel’nov [The structure of...
Properties of the class of measure separable compact spaces
We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure...
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.
Propriété de Baire de muni d’une nouvelle topologie et application à la construction d’ultrafiltres
Propriétés topologiques de et fantômes de finitude
Pro-reflections and pro-factorizations