For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,O) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Contin...

This work introduces the concepts of rectangular Menger probabilistic metric (RMPM) space and b-metric (RMPbM) as generalizations space, respectively. Some nonunique fixed-point coupled-fixed-point results for contractive mappings are provided. The findings extend improve outcomes presented in existing literature. main illustrated with examples, validated by means an application to a system int...

The intent of this paper is to establish a common fixed point theorem by using a new continuity condition in 2 Non-Archimedean Menger PM-space.This gives an alternative answer of the problem of Rhoades [6].Our result extends, generalizes and unifies several fixed point theorems on metric spaces, Menger probablistic-metric spaces and fuzzy metric spaces. Mathematics Subject Classification: 47H10...

Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group Z, whose square is not Mengerbounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded. This also answers some questions of Banakh, Nickolas, and Sanchis.

Employing the common property E.A , we prove some common fixed point theorems for weakly compatible mappings via an implicit relation in Menger PM spaces. Some results on similar lines satisfying quasicontraction condition as well as ψ-type contraction condition are also proved in Menger PM spaces. Our results substantially improve the corresponding theorems contained in Branciari, 2002 ; Rhoad...