Mutually Compactificable Topological Spaces

The Classes of Mutual Compactificability

Two disjoint topological spaces X , Y are mutually compactificable if there exists a compact topology on K = X ∪Y which coincides on X , Y with their original topologies such that the points x ∈ X , y ∈ Y have disjoint neighborhoods in K . The main problem under consideration is the following: which spaces X , Y are so compatible such that they together can form the compact space K? In this pap...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

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.  

$L$-Topological Spaces

‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...

Topological number for locally convex topological spaces with continuous semi-norms

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.