Paracompactness in countable products via the Souslin operation
Parametric extension of the Poincaré theorem
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.
Pasting topological spaces at one point
Let be a family of topological spaces and , for every . Suppose is the quotient space of the disjoint union of ’s by identifying ’s as one point . We try to characterize ideals of according to the same ideals of ’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let be an infinite cardinal. (1) Is there any ring and an ideal in such that is an irreducible intersection of prime ideals? (2) Is there...
P-embedding and product spaces
Perfect maps are exponentiable - categorically.
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...
Polishness of weak topologies generated by gap and excess functionals.
Power stability of k-spaces and compactness
Presheaves over the sets which need not be well ordered, functional separation of their inductive limits and their representation by sections
Prime extensions and nearness structures
Prime mappings, number of factors and binary operations [Book]
Probabilistic convergence spaces and generalized metric spaces.
Probability measure functors preserving infinite-dimensional spaces
Product properties for pairwise Lindelöf spaces.
Product proximities
Productively Fréchet spaces
We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.
Productivity of coreflective classes of topological groups
Every nontrivial countably productive coreflective subcategory of topological linear spaces is -productive for a large cardinal (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal , there are coreflective subcategories that are -productive and not -productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories...
Productivity of coreflective subcategories of uniform spaces
Products and measurable cardinals