In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.

In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...

We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regularLindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish so...

For a hereditary property P let kP(G) denote the number of forbidden subgraphs contained in G. A graph G is said to be weakly Psaturated, if G has the property P and there is a sequence of edges of G, say e1, e2, . . . , el, such that the chain of graphs G = G0 ⊂ G0+e1 ⊂ G1 + e2 ⊂ . . . ⊂ Gl−1 + el = Gl = Kn (Gi+1 = Gi + ei+1) has the following property: kP(Gi+1) > kP(Gi), 0 ≤ i ≤ l − 1. In thi...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

Every isometric property of Banach spaces preserved by real or complex interpolation is subspace-hereditary, and every isomorphic property of separable Banach spaces so preserved is quotient-hereditary. Introduction Many properties of Banach spaces are known to pass to interpolation spaces obtained from the real k-method of interpolation or from the complex method, completeness itself being the...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

Let P be a hereditary property. Let kP(G) denote the number of forbidden subgraphs, which are contained in G. A graph G is said to be weakly P-saturated, if G ∈ P and the edges of the complement of G can be labelled e1, e2, . . . , el in such way that for i= 0, 1, . . . , l− 1 the inequality kP(Gi+1)> kP(Gi) holds, whereG0=G,Gi+1=Gi + ei andGl =Kn. The minimum possible size of weakly P-saturate...

Let A be a Banach algebra. A is called ideally amenable if for every closed ideal I of A, the first cohomology group of A with coefficients in I* is trivial. We investigate the closed ideals I for which H1 (A,I* )={0}, whenever A is weakly amenable or a biflat Banach algebra. Also we give some hereditary properties of ideal amenability.