About new theorems in in this my blog post:
I’ve simplified this theorem:
Theorem A reloid $latex f$ is complete iff
$latex f = \bigsqcap^{\mathsf{RLD}} \left\{ \bigcup_{x \in \mathrm{Src}\, f}
(\{ x \} \times \langle T \rangle^{\ast} \{ x \}) \, |
\, T \in (\mathscr{P} \mathrm{Dst}\, f)^{\mathrm{Src}\, f}, \forall x \in
A : \langle T \rangle^{\ast} \{ x \} \in G (x) \right\} $.
into
Theorem A reloid $latex f$ is complete iff $latex f=(\mathsf{RLD})_{\mathrm{out}} g$ for a complete funcoid $latex g$.
For a proof see this note.
The next theorem:
Theorem A funcoid $latex f$ is complete iff
$latex f = \bigsqcap^{\mathsf{FCD}} \left\{ \bigcup_{x \in \mathrm{Src}\, f}
(\{ x \} \times \langle T \rangle^{\ast} \{ x \}) \, |
\, T \in (\mathscr{P} \mathrm{Dst}\, f)^{\mathrm{Src}\, f}, \forall x \in
A : \langle T \rangle^{\ast} \{ x \} \in G (x) \right\} $.
collapses into
Theorem $latex f=\bigsqcap^{\mathsf{FCD}} \mathrm{up}\, f$, what I proved long time ago.
So, I have removed this theorem from my writings.
Finally, I add the conjecture:
Conjecture A funcoid $latex f$ is complete iff $latex f=(\mathsf{FCD}) g$ for a complete reloid $latex g$.
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