On some conditions which imply the continuity of almost all sections
Let be an open interval, a topological space and a metric space. Some local conditions implying continuity and quasicontinuity of almost all sections of a function are shown.
On some fan-tightness type properties
Properties similar to countable fan-tightness are introduced and compared to countable tightness and countable fan-tightness. These properties are also investigated with respect to function spaces and certain classes of continuous mappings.
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 maps concerning -open sets.
On some operation on sets of mappings
On some problems of Borsuk
On some properties of the spaces of almost continuous functions.
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 some separation axioms and -closure
On some subclasses of Darboux functions
On some subspaces of the Helly space
On some test spaces in dimension theory
On some weak conditions of commutativity in common fixed point theorems.
On some weak monomorphisms and weak epimorphisms of pro-HTop*.
Related to Shape Theory, in a previous paper (1992) we studied weak monomorphisms and weak epimorphisms in the category of pro-groups. In this note we give some intrinsic characterizations of the weak monomorphisms and the weak epimorphisms in pro-HTop* in the case when one of the two objects of such a morphism is a rudimentary system.
On some weakened forms of continuity for multifunctions
On somewhat fuzzy semicontinuous functions
In this paper the concept of somewhat fuzzy semicontinuous functions, somewhat fuzzy semiopen functions are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are also given. More examples are given to illustrate the concepts introduced in this paper.
On spaces which have the shape of compact metric spaces
On spaces with binary normal subbase
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 stationary sets for certain generalizations of continuity