Skip to content
November 27, 2014 / porton

A new function which is a counter-example to a conjecture found

For this conjecture there was found a counter-example, see this online article.

The counter-example states that (\mathsf{RLD})_{\Gamma} f \sqsupset (\mathsf{RLD})_{\mathrm{in}} f \sqsupset (\mathsf{RLD})_{\mathrm{out}} f for funcoid f=(=)|_{\mathbb{R}}.

This way I discovered a new function (\mathsf{RLD})_{\Gamma} defined by the formula (\mathsf{RLD})_{\Gamma} f = \bigsqcap^{\mathsf{RLD}} \mathrm{up}^{\Gamma (\mathrm{Src}\,f ; \mathrm{Dst}\,f)} f.

While (\mathsf{RLD})_{\mathrm{in}} f and (\mathsf{RLD})_{\mathrm{out}} f have many cryptomorphisms (that is different but equivalent definitions) and lots of useful usages, all is known about (\mathsf{RLD})_{\Gamma} f is its definition and the formula (\mathsf{RLD})_{\Gamma} f \sqsupset (\mathsf{RLD})_{\mathrm{in}} f. It is unclear whether (\mathsf{RLD})_{\Gamma} is useful for anything.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: