Probabilistic convergence structures.
Probabilistic norms and statistical convergence of random variables.
Probabilistic Topologies Induced by L-Fuzzy Uniformities.
Product properties for pairwise Lindelöf spaces.
Product proximities
Productivity of coreflective subcategories of uniform spaces
Products in the category of apartness spaces
Products of Baire spaces revisited
Generalizing a theorem of Oxtoby, it is shown that an arbitrary product of Baire spaces which are almost locally universally Kuratowski-Ulam (in particular, have countable-in-itself π-bases) is a Baire space. Also, partially answering a question of Fleissner, it is proved that a countable box product of almost locally universally Kuratowski-Ulam Baire spaces is a Baire space.
Products of non--lower porous sets
In the present article we provide an example of two closed non--lower porous sets such that the product is lower porous. On the other hand, we prove the following: Let and be topologically complete metric spaces, let be a non--lower porous Suslin set and let be a non--porous Suslin set. Then the product is non--lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non--lower porous sets in topologically...
Products of normal spaces with Lašnev spaces
Products of proximites
Products of uniform spaces
Products of uniform spaces (Summary)
Products, the Baire category theorem, and the axiom of dependent choice
In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (i) The axiom of dependent choice. (ii) Products of compact Hausdorff spaces are Baire. (iii) Products of pseudocompact spaces are Baire. (iv) Products of countably compact, regular spaces are Baire. (v) Products of regular-closed spaces are Baire. (vi) Products of Čech-complete spaces are Baire. (vii) Products of pseudo-complete spaces are Baire.
Projective potencies and multiplicative extension operators
Prolongement d'une distance
Proper shape retracts
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 covering type and a factorization theorem
Property D and pseudonormality in first countable spaces
In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin’s Axiom type principle . We show that there is no such space in the usual Cohen model of the failure of CH.