The purpose of this paper is to present and investigate a new class topological spaces known as Sw*-regular spaces, by utilizing the concept Sw-regular sets some its properties. which introduced in 2009 L. S. Abddullah A. B. Khalaf [1], properly contained S*- regular space [2], [3], means that Sw*- stronger form regular. Several characterizations, properties relationships with other such as, Sw...

Matroids are a modern type of synthetic geometry in which the behavior of points, lines, planes, and higher-dimensional spaces are governed by combinatorial axioms. In this paper we describe our work on two well-known classification problems in matroid theory: determine all binary matroids M such that for every element e, either deleting the element ( ) or contracting the element ( ) is regular...

We obtain several Banach-Stone type theorems for vector-valued functions in this paper. Let X,Y be realcompact or metric spaces, E,F locally convex spaces, and φ a bijective linear map from C(X,E) onto C(Y, F ). If φ preserves zero set containments, i.e., z(f) ⊆ z(g)⇐⇒ z(φ(f)) ⊆ z(φ(g)), ∀ f, g ∈ C(X,E), then X is homeomorphic to Y , and φ is a weighted composition operator. The above conclusio...

The embedding theorems in anisotropic Besov-Lions type spaces Bp,θ(R ;E0,E) are studied; here E0 and E are two Banach spaces. The most regular spaces Eα are found such that the mixed differential operators Dα are bounded from Bp,θ(R ;E0,E) to B q,θ(R ;Eα), where Eα are interpolation spaces between E0 and E depending on α= (α1,α2, . . . ,αn) and l = (l1, l2, . . . , ln). By using these results t...

The domatic number of a graph G, denoted dom(G), is the maximum possible cardinality of a family of disjoint sets of vertices of G, each set being a dominating set of G. It is well known that every graph without isolated vertices has dom(G) ≥ 2. For every k, it is known that there are graphs with minimum degree at least k and with dom(G) = 2. In this paper we prove that this is not the case if ...

For a tournament T , let ν3(T ) denote the maximum number of pairwise edge-disjoint triangles (directed cycles of length 3) in T . Let ν3(n) denote the minimum of ν3(T ) ranging over all regular tournaments with n vertices (n odd). We conjecture that ν3(n) = (1 + o(1))n /9 and prove that n 11.43 (1− o(1)) ≤ ν3(n) ≤ n 9 (1 + o(1)) improving upon the best known upper bound of n −1 8 and lower bou...