σ−Connectivity in L−Topological Spaces

σ-Normality of Topological Spaces

$L$-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...

The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

P2-CONNECTEDNESS IN L-TOPOLOGICAL SPACES

In this paper, a certain new connectedness of L-fuzzy subsets inL-topological spaces is introduced and studied by means of preclosed sets. Itpreserves some fundamental properties of connected set in general topology.Especially the famous K. Fan’s Theorem holds.

Boundedness of linear order-homomorphisms in $L$-topological vector spaces

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...