This paper is a continuation of the work done in [9]. We are interested in the following question within the context of σ-ideals of σ-porous type. Let X be a metric space and let be a σ-ideal of subsets of X . Let S⊂ X be a Suslin set with S / ∈ . Does there exist a closed set F ⊂ S which is not in ? The answer is positive provided that X is locally compact and is a σ-ideal of σP-porous sets, w...

This article defines ranked soft sets and establishes their fundamental theory. new model of uncertain knowledge is a non-numerical yet powerful improvement sets. The relies on qualitative the basic parameterized description posed by We define relations between some existing models (N-soft sets, fuzzy probabilistic sets) that enhance set spirit with help additional quantities. Primary contribut...

We introduce the filter of locally closed unbounded sets and investigate its properties. As one application, we give a characterization of forcing notions that preserve stationary sets (in eo,). Also the local club filter and its variants lead to reflection principles for stationary sets. While the general reflection principle is related to Martin's Maximum of Foreman, Magidor and Shelah, the r...

A family of sets F is locally k-wide if and only if the width (as a poset ordered by inclusion) of F x = fU 2 F j x 2 U g is at most k for every x. The directed covering graph of a locally 1-wide family of sets is a forest of rooted trees. It is shown that if F is a locally k-wide family of subsets of f1; : : : ; ng, then jFj (2k) k?1 n. The proof involves a counting argument based on families ...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

This work aims to present the concept of infra soft $b$-open sets(IS-b-open sets) as a generalized new class open sets(IS-open sets). We first investigate their basic properties and study behaviours under homeomorphism maps finite product spaces. Then, we establish some operators such interior, closure, limit boundary using IS-b-open sets IS-$b$-closed sets. The relationships between them are i...