Atomic representations in function spaces and applications to pointwise multipliers and diffeomorphisms, a new approach

POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

We provide non-smooth atomic decompositions for Besov spaces Bsp,q(R n), s > 0, 0 < p, q ≤ ∞, defined via differences. The results are used to compute the trace of Besov spaces on the boundary Γ of bounded Lipschitz domains Ω with smoothness s restricted to 0 < s < 1 and no further restrictions on the parameters p, q. We conclude with some more applications in terms of pointwise multipliers. Ma...

On quasi $P$-spaces and their applications in submaximal and nodec spaces

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

A new class of function spaces on domains of R^d and its relations to classical function spaces

Preclosure operator and its applications in general topology

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...