In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

For a non-Archimedean locally convex space (E, τ), the finest locally convex topology having the same as τ convergent sequences and the finest locally convex topology having the same as τ compactoid sets are studied.

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...

The weak topology of a locally convex space (lcs) E is denoted by w. In this paper we undertake systematic study those lcs such that (E, w) (linearly) Eberlein–Grothendieck (see Definitions 1.2 and 3.1). following results obtained in our play key role: for every barrelled E, the (linearly Eberlein–Grothendieck) if only metrizable (E normable, respectively). main applications concern to continuo...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...