New easy theorem

I have added a new easy (but unnoticed before) theorem to my book: Proposition $latex (\mathsf{RLD})_{\mathrm{out}} f\sqcup (\mathsf{RLD})_{\mathrm{out}} g = (\mathsf{RLD})_{\mathrm{out}}(f\sqcup g)$ for funcoids $latex f$, $latex g$.

A step forward to solve an open problem

I am attempting to find the value of the node “other” in a diagram currently located at this file, chapter “Extending Galois connections between funcoids and reloids”. By definition $latex \mathrm{other} = \Phi_{\ast}(\mathsf{RLD})_{\mathrm{out}}$. A few minutes ago I’ve proved $latex (\Phi_{\ast}(\mathsf{RLD})_{\mathrm{out}})\bot = \Omega^{\mathsf{FCD}}$, that…

New short chapter

I’ve added a new short chapter “Generalized Cofinite Filters” to my book.