fuzzy rough n-ary subhypergroups are introduced and characterized.

This paper will use the concept of clearly visible to obtain a Krasnosel'skii-type theorem for the dimension of the kernel of a starshaped set, and the following result will be proved: For each fc and n, 1 < k < n, let f(n,n) = n -\1 and /(n, fc) = 2n if 1 < fc < n — 1. Let S be a nonempty compact set in Rn. Then for a fc with 1 < fc < n, dim ker S > fc if and only if every f(n, fc) points of b...

Let P<∞(N) be the set of all finite subsets of N, endowed with the product topology. A description of the compact subsets of P<∞(N) is given. Two applications of this result to Banach space theory are shown : (1) a characterization of the symmetric sequence spaces which embed into C(ω), and (2) a characterization, in terms of the Orlicz function M , of the Orlicz sequence spaces hM which embed ...

The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with 2 compact elements. We show that every algebraic lattice with at most 2 compact elements is a complete sublattice of Cl(X). 1. How complicated is the clone lattice? Fix a base set X and denote for all n ≥ 1 the set of all n-ary operations on X by O(n). Then O = ⋃ n≥1 O (n) is the set of all functions on X which ...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N -determined and conclud...

A topological space X, τ is said to be strongly compact if every preopen cover of X, τ admits a finite subcover. In this paper, we introduce a new class of sets called N-preopen sets which is weaker than both open sets and N-open sets. Where a subset A is said to be N-preopen if for each x ∈ A there exists a preopen set Ux containing x such that Ux − A is a finite set. We investigate some prope...

We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p ≥ 1 (resp. p = 0), and some closed subse...