ﻻ يوجد ملخص باللغة العربية
With a complete Heyting algebra $L$ as the truth value table, we prove that the collections of open filters of stratified $L$-valued topological spaces form a monad. By means of $L$-Scott topology and the specialization $L$-order, we get that the algebras of open filter monad are precisely $L$-continuous lattices.
Let $Sigma (X,mathbb{C})$ denote the collection of all the rings between $C^*(X,mathbb{C})$ and $C(X,mathbb{C})$. We show that there is a natural correlation between the absolutely convex ideals/ prime ideals/maximal ideals/$z$-ideals/$z^circ$-ideals
A.V.Arkhangelskii asked in 1981 if the variety $mathfrak V$ of topological groups generated by free topological groups on metrizable spaces coincides with the class of all topological groups. We show that if there exists a real-valued measurable card
A proper ideal $I$ in a commutative ring with unity is called a $z^circ$-ideal if for each $a$ in $I$, the intersection of all minimal prime ideals in $R$ which contain $a$ is contained in $I$. For any totally ordered field $F$ and a completely $F$-r
In this paper, we prove that: (1) Let $f:Grightarrow H$ be a continuous $d$-open surjective homomorphism; if $G$ is an $mathbb{R}$-factorizabile paratopological group, then so is $H$. Peng and Zhangs result cite[Theorem 1.7]{PZ} is improved. (2) Let
Let $M$ be an ANR space and $X$ be a homotopy dense subspace in $M$. Assume that $M$ admits a continuous binary operation $*:Mtimes Mto M$ such that for every $x,yin M$ the inclusion $x*yin X$ holds if and only if $x,yin X$. Assume also that there ex