📚 Recommended Mathematics Books
Topology (Munkres) | General Topology (Engelking) | Counterexamples in Topology | Rudin's AnalysisAs an Amazon associate, I earn from qualifying purchases.
Today I have noticed a new simple to prove theorem which is missing in my article:
Theorem If $latex ( \mathfrak{A}; \mathfrak{Z})$ is a join-closed filtrator and both $latex \mathfrak{A}$ and $latex \mathfrak{Z}$ are complete lattices, then for every $latex S \in \mathscr{P} \mathfrak{A}$
$latex \mathrm{Cor}’ \bigsqcap^{\mathfrak{A}} S = \bigsqcap^{\mathfrak{Z}} \langle \mathrm{Cor}’ \rangle S.$
Particularly if $latex S \in \mathscr{P} \mathfrak{Z}$, this theorem reduced to the formula:
$latex \mathrm{Cor}’ \bigsqcap^{\mathfrak{A}} S = \bigsqcap^{\mathfrak{Z}} S.$
Particularly the above formulas hold for filters on complete lattices.
I’ve added these theorems and their simple consequences to my book.
🔬 Advanced Mathematics References
- Sheaves in Geometry and Logic
- Categories for the Working Mathematician
- Stone Spaces
- Algebraic Topology (Hatcher)
- Concrete Mathematics
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