Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

We consider the non-orthodox proof rules of hybrid logic from the viewpoint of topological semantics. Topological semantics is more general than Kripke semantics. We show that the hybrid proof rule BG is topologically not sound. Indeed, among all topological spaces the BG rule characterizes those that can be represented as a Kripke frame (i.e., the Alexandroff spaces). We also demonstrate that,...

Let A and S denote the double arrow of Alexandroff Sorgenfrey line, respectively. We show that any homeomorphism h:mA→mA is locally (outside a nowhere dense set) product monotone embeddings hi:Ji⊆A→A(i∈m) followed by permutation coordinates. also prove symmetric products Fm(A) are not homogeneous for m≥2. This partially solves an open question A. Arhangel'skiǐ [1]. In contrast, we F2(S) homogen...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...