a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...