Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: composition of funcoids funcoids
 Posted by: porton on: July 12th, 2016

\begin{conjecture} $\forall H \in \operatorname{up} (g \circ f) \exists F \in \operatorname{up} f, G \in \operatorname{up} g : H \sqsupseteq G \circ F$ for every composable funcoids $f$ and $g$. \end{conjecture}

It's used notation from \href[Algebraic General Topology book]{http://www.mathematics21.org/algebraic-general-topology.html}

I claimed

It is easy to prove using the fact that funcoids are isomorphic to filters on certain boolean algebra and properties of generalized filter bases. Complete proof is now included in \href[my book]{http://www.mathematics21.org/algebraic-general-topology.html}.

My proof was with an error (the set in question is not a filter base as I claimed in the proof).

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/}

## Bibliography

*Victor Porton. \href [A blog post]{https://portonmath.wordpress.com/2016/07/12/new-conjecture/} % Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)

* indicates original appearance(s) of problem.