![](/files/happy5.png)
Another conjecture about reloids and funcoids ★★
Author(s): Porton
Definition
for reloid
.
![$ \square f = \bigcap^{\mathsf{RLD}} \mathrm{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $](/files/tex/233b3cef05580aee2ca00c357cfdbc67bacf126a.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
Conjecture
for every funcoid
.
![$ (\mathsf{RLD})_{\Gamma} f = \square (\mathsf{RLD})_{\mathrm{in}} f $](/files/tex/004185ca69576a6b46e10d7d0fb46c76b6c53c43.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
Note: it is known that (see below mentioned online article).
Keywords:
One-way functions exist ★★★★
Author(s):
Conjecture One-way functions exist.
Keywords: one way function
Funcoid corresponding to reloid through lattice Gamma ★★
Author(s): Porton
Conjecture For every reloid
and
,
:
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
![$ \mathcal{X} \in \mathfrak{F} (\operatorname{Src} f) $](/files/tex/1f01dd9f1243b55507248bea7af215e6469c00a8.png)
![$ \mathcal{Y} \in \mathfrak{F} (\operatorname{Dst} f) $](/files/tex/d7fa63ea4e0a3ad7a7f39a92a95ae4fe1906197d.png)
- \item
![$ \mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y} $](/files/tex/2f0c7dbaa1a5747d9bca753501374e8cd2500318.png)
![$ \langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigcap_{F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f} \langle F \rangle \mathcal{X} $](/files/tex/bcc925b41f94370c0dfe32107235c7a3435dcbf9.png)
It's proved by me in this online article.
Keywords: funcoid corresponding to reloid
Restricting a reloid to lattice Gamma before converting it into a funcoid ★★
Author(s): Porton
Conjecture
for every reloid
.
![$ (\mathsf{FCD}) f = \bigcap^{\mathsf{FCD}} (\Gamma (A ; B) \cap \operatorname{GR} f) $](/files/tex/d9afe4920809a29a644f5bc594e40f3313a8d527.png)
![$ f \in \mathsf{RLD} (A ; B) $](/files/tex/90326a901389c8760f7fa928fff117636a958338.png)
Keywords: funcoid corresponding to reloid; funcoids; reloids
Inner reloid through the lattice Gamma ★★
Author(s): Porton
Conjecture
for every funcoid
.
![$ (\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $](/files/tex/9c5b448dbc0964ca844d30e92247626e8d5420b5.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
Counter-example: for the funcoid
is proved in this online article.
Keywords: filters; funcoids; inner reloid; reloids