For every positive integer N and α∈[0,1), let B(N,α) denote the probabilistic model in which a random set A⊂{1,…,N} is constructed by choosing independently element of {1,…,N} with probability α. We prove that, as N⟶+∞, for A we have |AA|∼|A|2/2 1−o(1), if only iflog⁡(α2(log⁡N)log⁡4−1)log⁡log⁡N⟶−∞. This improves on theorem Cilleruelo, Ramana Ramaré, who proved above asymptotic between |AA| |A|2...

The notion of immune sets is extended to closed sets and Π 1 classes in particular. We construct aΠ 1 class with no computable member which is not immune. We show that for any computably inseparable sets A and B, the class S(A,B) of separating sets for A and B is immune. We show that every perfect thin Π 1 class is immune. We define the stronger notion of prompt immunity and construct an exampl...

In this paper, we introduce two different notions of generalized supra soft sets namely supra A--soft sets and supra soft locally closed sets in supra soft topological spaces, which are weak forms of supra open soft sets and discuss their relationships with each other and other supra open soft sets [{it International Journal of Mathematical Trends and Technology} (IJMTT), (2014) Vol. 9 (1):37--...

Metrizable spaces are studied in which every closed set is an α-limit for some continuous map and point. It shown that this property enjoyed by space containing sufficiently many arcs (formalized the notion of a with enough arcs), though such need not be arcwise connected. Further it preserved topological sums, products images quotients. However, positive results do hold metrizable obtained tho...

The purpose of the present paper is to introduce the concept of generalized closed sets in Čech closure spaces and investigate some of their characterizations. 2000 Mathematics Subject Classification: 54A05.

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

We prove compact-randomness of the intersection of a measurable familyof compact-random sets. This generalizes results on the intersection of countable families of random sets. The main tools are given by the theory of Souslin spaces and the idea of countable separation. An example of a random set is given by the energy spectrum of an electron in a disordered solid, or more generally by the spe...