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
Proximity approach to extension problems
Proximity classes of uniformities
PS-closed bitopological spaces
P-sets and minimal right ideals in ℕ*
Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...
Pseudocompact spaces with a -point-finite base are metrizable
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.
Pseudocompactness - from compactifications to multiplication of borel sets
Pseudouniform topologies on given by ideals
Given a Tychonoff space , a base for an ideal on is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.
Quantification of topological concepts using ideals.