‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...

Let 5 be a set in an «-dimensional Euclidean space, E„. The following concept was used by Horn and Valentine [2] in their study of L sets, and it provides the basis of this investigation. Definition 1. A set VES is a set of visibility in S if, given any point p ES, there exists a point qEV such that the closed segment pqQS. Notation. Given a point xES, let Vix) denote a continuum1 of visibility...

A MAD (maximal almost disjoint) family is an infinite subset A of the infinite subsets of ω = {0, 1, 2, . . . , } such that any two elements of A intersect in a finite set and every infinite subset of ω meets some element of A in an infinite set. A Q-set is an uncountable set of reals such that every subset is a relative Gδ set. It is shown that it is relatively consistent with ZFC that there e...

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...

Then Γ acts cocompactly on X and X , and the orbit spaces X/Γ and X /Γ are closed manifolds with contractible universal covers. The only nontrivial homotopy groups are thus the fundamental groups, π1(X/Γ) ∼= Γ ∼= π1(X /Γ). It follows that there is a homotopy equivalence X/Γ X /Γ which can be lifted to a map f : X X . This map f can then be shown to be a quasi-isometry. Recall that a (not necess...

In this paper a bijection between the set of prime ideals of a Leavitt path algebra L K (E) and a certain set which involves maximal tails in E and the prime spectrum of K[x, x −1 ] is established. Necessary and sufficient conditions on the graph E so that the Leavitt path algebra L K (E) is primitive are also found.

Then Γ acts cocompactly on X and X , and the orbit spaces X/Γ and X /Γ are closed manifolds with contractible universal covers. The only nontrivial homotopy groups are thus the fundamental groups, π1(X/Γ) ∼= Γ ∼= π1(X /Γ). It follows that there is a homotopy equivalence X/Γ X /Γ which can be lifted to a map f : X X . This map f can then be shown to be a quasi-isometry. Recall that a (not necess...