In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter T (E) = P (E,Ω) + G (E) with a volume constraint. Here Ω is any open subset of Rn with n ≥ 2, G is a lower semicontinuous function on sets of finite perimeter satisfying a condition that G (E) ≤ G (F ) + C |E∆F | among all sets of finite perimeter with equal volume. We show that under the condition β >...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

We introduce the class of linearly S-closed spaces as a proper subclass H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called if only any semi-open chain cover posses member dense in space. It shown that extremally disconnected coincide. gave characterizations these terms s-accumulation points filter bases complete families open subsets. While re...

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

in this paper‎, ‎we show the stability of gustafson‎, ‎weidmann‎, ‎kato‎, ‎wolf‎, ‎schechter and browder essential spectrum of bounded linear operators on banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $u$ such $gamma(u^m)

— Given a closed (not necessarly compact) semi-algebraic set X in Rn, we construct a non-negative semi-algebraic C2 function f such that X=f−1(0) and such that for δ > 0 sufficiently small, the inclusion of X in f−1([0, δ]) is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of X. Résumé. — Étant donné un ensemble semi-algébrique fermé (non nécessairement co...