Abstract We investigate the relation between concentration and product of metric measure spaces. have natural question whether, for two concentrating sequences spaces, sequence their spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. obtain a complete this question.

This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

Let n = (n1, . . . , nr). The quotient space Pn := Sn1× · · ·×Snr/(x ∼ −x) is what we call a projective product space. We determine the integral cohomology ring H∗(Pn) and the action of the Steenrod algebra on H∗(Pn;Z2). We give a splitting of ΣPn in terms of stunted real projective spaces, and determine when Si is a product factor of Pn. We relate the immersion dimension and span of Pn to the ...

A topological space is called paracompact (see [2 J) if (i) it is a Hausdorff space (satisfying the T2 axiom of [l]), and (ii) every open covering of it can be refined by one which is "locally finite" ( = neighbourhood-finite; that is, every point of the space has a neighbourhood meeting only a finite number of sets of the refining covering). J. Dieudonné has proved [2, Theorem 4] that every se...

The theory of influence and sharp threshold is a key tool in probability and probabilistic combinatorics, with numerous applications. One significant aspect of the theory is directed at identifying the level of generality of the product probability space that accommodates the event under study. We derive the influence inequality for a completely general product space, by establishing a relation...