Little changes in my math book
The section “Filters on a Set” of the preprint of my math book is rewritten noting the fact that $latex \mathrm{Cor}\, \mathcal{A} = \uparrow^{\mathrm{Base} ( \mathcal{A})} \bigcap \mathcal{A}$.
New theorem about core part of funcoids and reloids
Today I’ve proved a new little theorem: Theorem $latex \mathrm{Cor} ( \mathsf{FCD}) g = ( \mathsf{FCD}) \mathrm{Cor}\, g$ for every reloid $latex g$. Conjecture For every funcoid $latex g$ $latex \mathrm{Cor} ( \mathsf{RLD})_{\mathrm{in}} g = ( \mathsf{RLD})_{\mathrm{in}} \mathrm{Cor}\, g$; $latex \mathrm{Cor} ( \mathsf{RLD})_{\mathrm{out}} g = ( \mathsf{RLD})_{\mathrm{out}} \mathrm{Cor}\, g$. See my book.
A theorem generalized
I generalized a theorem in the preprint article “Filters on posets and generalizations” on my Algebraic General Topology site. The new theorem is formulated as following: Theorem If $latex (\mathfrak{A}; \mathfrak{Z})$ is a join-closed filtrator and $latex \mathfrak{A}$ is a meet-semilattice and $latex \mathfrak{Z}$ is a complete lattice, then $latex \mathrm{Cor}’ (a \cap^{\mathfrak{A}} b) = […]
New conjecture about core parts of filters
Conjecture $latex \mathrm{Cor}\bigcup^{\mathfrak{F}} S=\bigcup\langle \mathrm{Cor}\rangle S$ for any set $latex S$ of filter objects on a set. See this wiki site for definitions of used terms.