A notion of reticulation which provides topological properties on algebras has introduced on commutative rings in 1980 by Simmons in [5]. For a given commutative ring A, a pair (L, λ) of a bounded distributive lattice and a mapping λ : A → L satisfying some conditions is called a reticulation on A, and the map λ gives a homeomorphism between the topological space Spec(A) consisting of prime fil...

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This ...

The simplest bimodal combination of unimodal logics L1 and L2 is their fusion, L1 ⊗ L2, axiomatized by the theorems of L1 for 1 and of L2 for 2, and the rules of modus ponens, substitution and necessitation for 1 and for 2. Shehtman introduced the frame product L1 × L2, as the logic of the products of certain Kripke frames: these logics are two-dimensional as well as bimodal. Van Benthem, Bezha...

Considering a frame L, we introduce the notions of stratified L-semi-topological neighborhood group, stratified L-quasi-topological neighborhood group, and stratified L-quasi-bi-topological neighborhood group. In so doing, we look at the notion of stratified L-right (left) semi-topological neighborhood group, provide some basic facts, and present a construction of a stratified L-right semi-topo...

We study fixed point theorems for maps which satisfy a property of stretching a suitably oriented topological space Z along the paths connecting two disjoint subsets Z− l and Z− r of Z . Our results reconsider and extend previous theorems in [56, 59, 60] where the case of two-dimensional cells (that is topological spaces homeomorphic to a rectangle of the plane) was analyzed. Applications are g...

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

in this paper, using pre-semi-open l-sets and their inequality, a new notion of ps-compactness is introduced in l-topological spaces, where l is a complete de morgan algebra. this notion does not depend on the structure of the basis lattice l and l does not need any distributivity.

A [semi-]continuous real function of a frame (locale) L has up to now been understood as a frame homomorphism from the frame L(R) of reals into L [as a frame homomorphism (modulo some conditions) from certain subframes of L(R) into L]. Thus, these continuities involve different domains. It would be desirable if all these continuities were to have L(R) as a common domain. This paper demonstrates...