Convexity numbers of closed sets in $\mathbb R^n$

CONVEXITY NUMBERS OF CLOSED SETS IN Rn

Convexity Numbers of Closed Sets in R

For n > 2 let In be the σ-ideal in P(nω) generated by all sets which do not contain n equidistant points in the usual metric on nω. For each n > 2 a set Sn is constructed in Rn so that the σ-ideal which is generated by the convex subsets of Sn restricted to the convexity radical K(Sn) is isomorphic to In. Thus cov(In) is equal to the least number of convex subsets required to cover Sn — the con...

On Convexity of Right-Closed Integral Sets

Let N denote the set of non-negative integers. A set of non-negative, n-dimensional integral vectors, M ⊂ N, is said to be right-closed, if ((x ∈ M) ∧ (y ≥ x) ∧ (y ∈ N)) ⇒ (y ∈ M). In this paper, we present a polynomial time algorithm for testing the convexity of a right-closed set of integral vectors, when the dimension n is fixed. Right-closed set of integral vectors are infinitely large, by ...

Some new properties of fuzzy strongly ${{g}^{*}}$-closed sets and $delta {{g}^{*}}$-closed sets in fuzzy topological spaces

‎In this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.

Some Generalizations of Locally Closed Sets

Arenas et al. [1] introduced the notion of lambda-closed sets as a generalization of locally closed sets. In this paper, we introduce the notions of lambda-locally closed sets, Lambda_lambda-closed sets and lambda_g-closed sets and obtain some decompositions of closed sets and continuity in topological spaces.