On Baire approximations of normal integrands
On continuity and monotonicity of Darboux functions
On dyadic spaces and almost Milyutin spaces
On embeddings into where is Lindelöf
A.V. Arkhangel’skii asked that, is it true that every space of countable tightness is homeomorphic to a subspace (to a closed subspace) of where is Lindelöf? denotes the space of all continuous real-valued functions on a space with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace of ...
On hedgehog-topologically fine uniform spaces
On homomorphisms of groups of integer-valued functions.
On -spaces and -spaces
In this note we study the relation between -spaces and -spaces and prove that a -space with a -hereditarily closure-preserving -network consisting of compact subsets is a -space, and that a -space with a point-countable -network consisting of compact subsets need not be a -space.
On minimal ideals in the ring of real-valued continuous functions on a frame
Let be the ring of real-valued continuous functions on a frame . The aim of this paper is to study the relation between minimality of ideals of and the set of all zero sets in determined by elements of . To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame , it is proved that the -ring is isomorphic to the -ring of all real continuous functions on the topological space . Finally, a one-one correspondence is...
On nowhere density of the class of somewhat continuous functions in
On polynomial mappings into spheres
On quasi-uniform convergence of a sequence of s.q.c. functions
On Scheepers' conjecture
On sets of points of semicontinuity in fine topologies generated by an ideal
On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.
For a completely regular space X, C*(X) denotes the algebra of all bounded real-valued continuous functions over X. We consider the topology of uniform convergence over C*(X).When K is a compact space, the Stone-Weierstrass and Kakutani-Stone theorems provide necessary and sufficient conditions under which a function f ∈ C*(K) can be uniformly approximated by members of an algebra, lattice or vector lattice of C*(K). In this way, the uniform closure and, in particular, the uniform density of algebras...
On some representations of almost everywhere continuous functions on
It is proved that the following conditions are equivalent: (a) f is an almost everywhere continuous function on ; (b) f = g + h, where g,h are strongly quasicontinuous on ; (c) f = c + gh, where c ∈ ℝ and g,h are strongly quasicontinuous on .
On spaces with the ideal convergence property
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.
On strongly preirresolute topological vector spaces
In the paper we obtain several characteristics of pre- of strongly preirresolute topological vector spaces and show that the extreme point of a convex subset of a strongly preirresolute topological vector space lies on the boundary.
On the Baire order problem for a linear lattice of functions
On the class of functions having infinite limit on a given set
On the continuity and monotonicity of restrictions of connected functions