![](/files/happy5.png)
Conjecture (solved) If
then
for every funcoid
and atomic f.o.
and
on the source and destination of
correspondingly.
![$ a \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} b \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f $](/files/tex/0435b975c85d609a344bf2dcbd5cfacf4cccef40.png)
![$ a \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} b \subseteq f $](/files/tex/540c8fb9c1b2fbbe12b46d35f6cb7aa3511a989b.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
![$ a $](/files/tex/b1d91efbd5571a84788303f1137fb33fe82c43e2.png)
![$ b $](/files/tex/b94226d9717591da8122ae1467eda72a0f35d810.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
A stronger conjecture:
Conjecture If
then
for every funcoid
and
,
.
![$ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f $](/files/tex/dbf9c288bef784da3d3a5d335b1ca97c01219f4e.png)
![$ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} \mathcal{B} \subseteq f $](/files/tex/a4b67c268d0f2a939ae1d63a31fd57a3945e4ec5.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
![$ \mathcal{A} \in \mathfrak{F} \left( \ensuremath{\operatorname{Src}}f \right) $](/files/tex/52f123c93b14e31b514495ac39d8781cd597c443.png)
![$ \mathcal{B} \in \mathfrak{F} \left( \ensuremath{\operatorname{Dst}}f \right) $](/files/tex/7310f0f823acdb77df75af0f8c924cdd8df0fe53.png)
See Algebraic General Topology for definitions of used concepts.
Bibliography
*Victor Porton. Algebraic General Topology
* indicates original appearance(s) of problem.