📚 Recommended Mathematics Books
Topology (Munkres) | General Topology (Engelking) | Counterexamples in Topology | Rudin's AnalysisAs an Amazon associate, I earn from qualifying purchases.
Just a few seconds ago I had an idea how to generalize both funcoids and reloids.
Consider
- a precategory, whose objects are sets
- product $latex \times$ of filters on sets ranging in morphisms of this category
- operations $latex \mathrm{dom}$ and $latex \mathrm{im}$ from the morphisms of our precategory to filters on our objects (sets)
This axiomatic system is so powerful that it allows to define $latex \langle f\rangle$ for a funcoid $latex f$:
$latex \langle f\rangle\mathcal{X} = \mathrm{im}(f\circ(1^\mathfrak{F}\times^\mathsf{FCD}\mathcal{X}))$.
🔬 Advanced Mathematics References
- Sheaves in Geometry and Logic
- Categories for the Working Mathematician
- Stone Spaces
- Algebraic Topology (Hatcher)
- Concrete Mathematics
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However this axiomatic system is probably too weak to prove $latex \langle g\rangle\langle f\rangle\mathcal{X} = \langle g\circ f\rangle\mathcal{X}$. We need additional axioms.