We prove the topological invariance of the combinatorial Euler characteristic of ominimal sets with the help of a canonical, topologically defined stratification of o-minimal sets by locally compact ones. Introduction. Let Bn be the collection of semi-algebraic subsets of R, i.e. sets definable by a finite boolean combination of polynomial equalities and inequalities. The Bn, n ∈ N, satisfy (i)...

Semi-linear sets, which are finitely generated subsets of the monoid (Z,+), have numerous applications in theoretical computer science. Although semi-linear sets are usually given implicitly, by formulas in Presburger arithmetic or by other means, the effect of Boolean operations on semi-linear sets in terms of the size of generators has primarily been studied for explicit representations. In t...

In this paper, a condition which ensures the existence of fuzzy simply open sets in $P$- space is obtained. It established that disjoint $G_{\delta}$-sets $P$-space are cs dense sets. A for strongly irresolvable and globally disconnected to become hyperconnected D-Baire space. obtained extremally disconnected, semi-$P$ does not have $G_{\delta}$-sets.

The lattice Lu of upper semicontinuous convex normal functions with convolution ordering arises in studies of type-2 fuzzy sets. In 2002, Kawaguchi and Miyakoshi [Extended t-norms as logical connectives of fuzzy truth values, Multiple-Valued Logic 8(1) (2002) 53–69] showed that this lattice is a complete Heyting algebra. Later, Harding et al. [Lattices of convex, normal functions, Fuzzy Sets an...

A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...

In this paper, we introduce the notions of fuzzy γ-I-open sets and fuzzy γ-I-continuous functions to obtain a decomposition of fuzzy semi-I-continuity. We also investigated the fundamental properties of such functions.