In this paper, we first define the notion of $\mathcal{F}$-cosmall quotient for an additive exact substructure $\mathcal{F}$ structure $\mathcal{E}$ in category $\mathcal{A}$. We show that every is right minimal some cases. also give definition $\mathcal{F}$-superfluous and relate it approximation modules. As application, investigate our results a pure-exact $\mathcal{F}$.

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

We show that call-by-need is observationally equivalent to weak-head needed reduction. The proof of this result uses a semantical argument based on a (non-idempotent) intersection type system called $\mathcal{V}$. Interestingly, system $\mathcal{V}$ also allows to syntactically identify all the weak-head needed redexes of a term.

In this paper we deepen, in the setting of coherence, some results obtained recent papers on notion p-entailment Adams and its relationship with conjoined iterated conditionals. We recall that conditionals are suitably defined framework conditional random quantities. Given a family $\mathcal{F}$ $n$ events $\{E_1|H_1,\ldots, E_n|H_n\}$ denote by $\mathscr{C}(\mathcal{F})=(E_1|H_1)\wedge \cdots ...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

Let $d\geq2$ be an integer. The set $\mathbf{F}(d)$ of foliations degree $d$ on the complex projective plane can identified with a Zariski's open space dimension $d^2+4d+2$ which $\mathrm{Aut}(\mathbb P^2_{\mathbb C})$ acts. We show that there are exactly two orbits $\mathcal{O}(\mathcal{F}_{1}^{d})$ and $\mathcal{O}(\mathcal{F}_{2}^{d})$ minimal $6$, necessarily closed in $\mathbf{F}(d)$. This...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...