‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

The two-dimensional system of nonlinear differential equations (A) x′′ = p(t)y, y′′ = q(t)x , with positive exponents α and β satisfying αβ < 1 is analyzed in the framework of regular variation. Under the assumption that p(t) and q(t) are nearly regularly varying it is shown that system (A) may possess three types of positive solutions (x(t), y(t)) which are strongly monotone in the sense that ...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

We consider flows (X,T), given by actions (t,x)→tx, on a compact metric space X with discrete T as an acting group. study new class of - the Strongly Rigid (SR) flows, that are properly contained in distal (D) and contain all equicontinuous (EQ) flows. Thus, EQflows⫋SRflows⫋Dflows. The concepts equicontinuity, strong rigidity distality coincide for induced flow (2X,T). observe strongly rigid (X...

Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...

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