Given a generalized continuum $X$, let $\operatorname{CL}_{{\rm F}}(X)$ and $\operatorname{C}(X)$ denote its hyperspaces of (non-empty) closed subsets subcontinua, respectively, with the Fell topology ($=$ Vietoris on $\operatorname{C}(X)

various authors have considered the zero-rest-mass equation and the contour integral representation of its solutions. ferber generalized these equations to supertwistor spaces with 2n odd components so that with n=o we get the standard ungraded twistors of penrose. in this paper we use the batchelor theorem toconstruct the natural super twistor space with coarse topology with underlying standar...

Rough set theory can be generalized by induced topology through equivalence relations. Motivated the work of generalization rough via topology, concept and properties $ \tau-\mathfrak{K} $-fuzzy open (closed) sets are proposed. Considering sets, we have obtained lower upper approximations also proved their properties. represented as $-open \alpha level sets. The fuzzy on basis binary relation c...

Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric and generalized ultrametric in logic. In particular we study approximation chains in an ultrametric ...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

Various authors have considered the Zero-rest-mass equation and the contour integral representation of its solutions. Ferber generalized these equations to supertwistor spaces with 2N odd components so that with N=O we get the standard ungraded twistors of Penrose. In this paper we use the Batchelor theorem toconstruct the natural super Twistor space with coarse topology with underlying sta...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

We study a generalized notion of topology which evolved from applications in the area of logic programming semantics. The generalization is obtained by relaxing the requirement that a neighbourhood of a point includes the point itself, and by allowing neighbourhoods of points to be empty. We show that it is meaningful to discuss neighbourhoods, convergence, and continuity in these spaces. A gen...

We study a generalized notion of topology which evolved from applications in the area of logic programming semantics The generalization is obtained by relaxing the requirement that a neighbourhood of a point includes the point itself and by allowing neighbourhoods of points to be empty We show that it is meaningful to discuss neighbourhoods convergence and continuity in these spaces A generaliz...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...