I’ve sent to personnel of Open Problem Garden the following proposal email:

Please add in each problem page a PayPal donation button. The money
collected for a problem should be directed to the person which first solves
the problem.

One additional advantage is that this would provide a way to sort problems
by importance: most funded problem are these which seem most important.

This way your site would additionally become a central hub of math prizes.

I think, it is a very good idea.

I have announced that I have proved that Category of continuous maps between endofuncoids is cartesian closed. This was a fake alarm, my proof was with a crucial error.

Now I have put the problem and some ideas how to prove it in a wiki.

So I announce a new project akin to Polymath Project. Please participate in solving my open problem.

I rough draft article I prove that the category of continuous maps between endofuncoids is cartesian closed.

Whether the category of continuous maps between endoreloids is cartesian closed, is yet an open problem.

There are two changes in Products in dagger categories with complete ordered Mor-sets draft article:

1. I’ve removed the section on relation of subatomic product with categorical product saying that for funcoids they are the same. No, they are not the same. My claim that they are the same was false.

2. Added section “Special case of funcoids” with a theorem and two new open problems:

Proposition $\prod^{\mathsf{FCD}} a \mathrel{\left[ \prod f \right]} \prod^{\mathsf{FCD}} b \Leftrightarrow \forall i \in \mathrm{dom}\, f : a_i \mathrel{[ f_i]} b_i$ for an indexed family $f$ of funcoids and indexed families $a$ and $b$ of filters where $a_i \in \mathfrak{F} ( \mathrm{Src}\, f_i)$, $b_i \in \mathfrak{F} ( \mathrm{Dst}\, f_i)$ for every $i \in \mathrm{dom}\, f$.

Conjecture $\left\langle \prod f \right\rangle x = \prod^{\mathsf{FCD}}_{i \in \mathrm{dom}\, f} \langle f_i \rangle \Pr^{\mathsf{FCD}}_i x$ for an indexed family $f$ of funcoids and $x \in \mathrm{atoms}^{\mathsf{FCD} ( \lambda i \in \mathrm{dom}\, f : \mathrm{Src}\, f_i)}$ for every $n \in \mathrm{dom}\, f$.

A weaker conjecture:

Conjecture $\langle f \times g \rangle x = \langle f \rangle \mathrm{dom}\, x \times^{\mathsf{FCD}} \langle g \rangle \mathrm{im}\, x$ for funcoids $f$ and $g$ and $x \in \mathrm{atoms}^{\mathsf{FCD} ( \mathrm{Src}\, f ; \mathrm{Src}\, g)}$.

On the task formulated in this blog post:

An attempt to prove that $\mathrm{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections (see http://portonmath.tiddlyspace.com/#%5B%5BSingularities%20funcoids%3A%20some%20special%20cases%5D%5D)

http://portonmath.tiddlyspace.com/#%5B%5BSingularities%20funcoids%3A%20special%20cases%20proof%20attempts%5D%5D

I feel that there are certain similarities between God and time machine.