A hypercyclicity criterion for non-metrizable topological vector spaces

Proto-metrizable fuzzy topological spaces

s-Topological vector spaces

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

Topological Mixing and Hypercyclicity Criterion for Sequences of Operators

For a sequence {Tn} of continuous linear operators on a separable Fréchet space X, we discuss necessary conditions and sufficient conditions for {Tn} to be topologically mixing, and the relations between topological mixing and the Hypercyclicity Criterion. Among them are: 1) topological mixing is equivalent to being hereditarily densely hypercyclic; 2) the Hypercyclicity Criterion with respect ...

Basic Properties of Metrizable Topological Spaces

We continue Mizar formalization of general topology according to the book [16] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also de...

On $beta-$topological vector spaces

We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.