In the ideal topological spaces (X, ?, I) and (Y, J, ?), we define (I, J)-irresolute function, weakly-(I, J)-irresolute, strongly-(I, functions, semi-I-open sets quasi-H-closed modulo I. We discuss properties of function mapping connected, closed, compact I semi-I-isolated points. J)-Homeomorphisim on presemi-I-open closure subsets are explored in this paper.

LetH be a real Hilbert space with inner product 〈·, ·〉 and norm ‖ · ‖, and let C be a nonempty closed convex subset of H. Recall that a mapping T : H → H is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖ for all x, y ∈ H. The set of fixed points of T is Fix T : {x ∈ H : Tx x}. T : H → H is said to be quasi-nonexpansive if Fix T is nonempty and ‖Tx − p‖ ≤ ‖x − p‖ for all x ∈ H and p ∈ Fix T . Given ...

in this paper we define ( , ) k  q -fuzzy h -sub hemirings, ( , ) k  q -fuzzy h -ideals, ( , ) k  q - fuzzy     h -bi-ideals and ( , ) k  q -fuzzy h -quasi-ideals. we characterize h -hemiregular and h -intrahemiregular hemirings by the properties of their     ( , ) k  q -fuzzy h -ideals, ( , ) k  q -fuzzy h -bi-ideals and     ( , ) k  q -fuzzy h -quasi-...

Let H 0(X) (H(X)) denote the set of all (nonempty) closed subsets of X endowed with the Vietoris topology. A basic problem concerning H(X) is to characterize those X for which H(X) is countably compact. We conjecture that u-compactness of X for some u ∈ ω∗ (or equivalently: all powers of X are countably compact) may be such a characterization. We give some results that point into this direction...

In this paper we introduce b− open, b− closed, quasi b− open, quasi b − closed, strongly b − open and strongly b − closed functions and investigate properties and characterizations of these new types of functions.