On the existence of P-points in the Stone-Čech compactification of integers
On the existence of true uniform ultrafilters
We shall show that there is an ultrafilter on singular with countable cofinality, which cannot be reached from the set of all subuniform ultrafilters by iterating the closure of sets of size .
On the existence of -primitives on arbitrary metric spaces
On the existence problem in the algebraic approach to quantum field theory
On the extensibility of closed filters in T spaces and the existence of well orderable filter bases
We show that the statement CCFC = “the character of a maximal free filter of closed sets in a space is not countable” is equivalent to the Countable Multiple Choice Axiom CMC and, the axiom of choice AC is equivalent to the statement CFE = “closed filters in a space extend to maximal closed filters”. We also show that AC is equivalent to each of the assertions: “every closed filter in a space extends to a maximal closed filter with a well orderable filter base”, “for every set ,...
On the extension and generation of set-valued mappings of bounded variation
We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...
On the extension of continuous functions
On the extensions of uniformly continuous mappings
On the extent of separable, locally compact, selectively (a)-spaces
The author has recently shown (2014) that separable, selectively (a)-spaces cannot include closed discrete subsets of size . It follows that, assuming CH, separable selectively (a)-spaces necessarily have countable extent. However, in the same paper it is shown that the weaker hypothesis "" is not enough to ensure the countability of all closed discrete subsets of such spaces. In this paper we show that if one adds the hypothesis of local compactness, a specific effective (i.e., Borel) parametrized...
On the extent of star countable spaces
For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have...
On the External Characterization of Topological Functors.
On the fixed point property for set-valued mappings of hereditarily decomposable continua
On the fixed points in an -limit set
Let and be closed subsets of [0,1] with a subset of the limit points of . Necessary and sufficient conditions are found for the existence of a continuous function such that is an -limit set for and is the set of fixed points of in .
On the foundations of k-group theory [Book]
On the foundations of Topology
On the Fréchet-Urysohn property in spaces of continuous functions
On the functionally countable subalgebra of C(X)
On the functor of order-preserving functionals
We introduce a functor of order-preserving functionals which contains some known functors as subfunctors. It is shown that this functor is weakly normal and generates a monad.
On the fundamental dimension of approximatively 1-connected compacta
On the fundamental dimension of the Cartesian product of compacta with the fundamental dimension 2