Funcoidal products inside an inward reloid

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords: inward reloid
Recomm. for undergrads: no
Posted by: porton
on: January 1st, 2012

\begin{conjecture} (solved) If $a \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} b \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f$ then $a \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} b \subseteq f$ for every funcoid $f$ and atomic f.o. $a$ and $b$ on the source and destination of $f$ correspondingly. \end{conjecture}

A stronger conjecture:

\begin{conjecture} If $\mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f$ then $\mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} \mathcal{B} \subseteq f$ for every funcoid $f$ and $\mathcal{A} \in \mathfrak{F} \left( \ensuremath{\operatorname{Src}}f \right)$, $\mathcal{B} \in \mathfrak{F} \left( \ensuremath{\operatorname{Dst}}f \right)$. \end{conjecture}

See \href [Algebraic General Topology]{http://www.mathematics21.org/algebraic-general-topology.html} for definitions of used concepts.

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Bibliography

*Victor Porton. \href[Algebraic General Topology]{http://www.mathematics21.org/algebraic-general-topology.html} % (Put an empty line between individual entries)


* indicates original appearance(s) of problem.