In this paper, the notions of countable S∗-compactness is introduced in L-topological spaces based on the notion of S∗-compactness. An S∗-compact L-set is countably S∗-compact. If L = [0, 1], then countable strong compactness implies countable S∗-compactness and countable S∗-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S∗-compact L-s...

Heating and cooling systems account for a considerable portion of the energy consumed domestic reasons in Europe. Burning fossil fuels is main way to produce this energy, which has detrimental effect on environment. It essential consider building’s characteristics when determining how much heating necessary. As result, study related buildings’ characteristics, such as type required maintaining ...

In this paper, a new notion of sequential compactness is introduced in L-topological spaces, which is called sequentially S∗-compactness. If L = [0, 1], sequential ultra-compactness, sequential N-compactness and sequential strong compactness imply sequential S∗-compactness, and sequential S∗-compactness implies sequential F-compactness. The intersection of a sequentially S∗-compact L-set and a ...

in this paper, the concept of countably near ps-compactness inl-topological spaces is introduced, where l is a completely distributive latticewith an order-reversing involution. countably near ps-compactness is definedfor arbitrary l-subsets and some of its fundamental properties are studied.

we obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. also weconsider relations kadec-klee property and shur property with this objects.these theorems are extend of papers mohebi and narayana.

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...