📚 Recommended Mathematics Books
Topology (Munkres) | General Topology (Engelking) | Counterexamples in Topology | Rudin's AnalysisAs an Amazon associate, I earn from qualifying purchases.
I’ve proved the following conjecture:
Theorem Let $latex f$ be a staroid such that $latex (\mathrm{form}\, f)_i$ is an atomic lattice for
each $latex i \in \mathrm{arity}\, f$. We have
$latex \displaystyle L \in \mathrm{GR}\, f \Leftrightarrow \mathrm{GR}\, f \cap
\prod_{i \in \mathrm{dom}\, \mathfrak{A}} \mathrm{atoms}\, L_i \neq \emptyset $
\prod_{i \in \mathrm{dom}\, \mathfrak{A}} \mathrm{atoms}\, L_i \neq \emptyset $
for every $latex L \in \prod_{i \in \mathrm{arity}\, f} (\mathrm{form}\,
f)_i$ (where upgrading is taken on the primary filtrator).
The proof is based on transfinite recursion. See this online article for the proof.
The above proof was with an error. Now there is a counter-example in the same article.
🔬 Advanced Mathematics References
- Sheaves in Geometry and Logic
- Categories for the Working Mathematician
- Stone Spaces
- Algebraic Topology (Hatcher)
- Concrete Mathematics
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