Let X,Y be normed spaces. The set of bounded linear operators is noted as L(X,Y ). Let now D = D(A) ⊂ X be a linear subspace, and A : D −→ Y a linear (not necessarily bounded!) operator. Notation: (A,D(A)) : X −→ Y Definition: G(A) := {(x,Ax) |x ∈ D} is called the graph of A. Obviously, G(A) is a linear subspace of X × Y . The linear operator A is called closed if G(A) is closed in X × Y . The ...

The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP.

Our primary query is to Önd conditions under which the closure of a preorder on a topological space remains transitive. We study this problem for translation invariant preorders on topological groups. The results are fairly positive; we Önd that the closure of preorders and normal-orders remain as such in this context. The same is true for factor orders as well under quite general conditions. I...

Due to importance of the concepts of θ-closure and δ-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy δ-closure by using the concept of quasicoincidence in fuzzy topological spaces. In this paper, we will introduce the concept of δ-closure in intuitionistic fuzzy topological spaces, which is a g...

We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is inspired by the methods of the author utilizing the osculating spaces of Veronese varieties. Linear network coding transmits information in terms of a basis of a ...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...