📚 Recommended Mathematics Books
Topology (Munkres) | General Topology (Engelking) | Counterexamples in Topology | Rudin's AnalysisAs an Amazon associate, I earn from qualifying purchases.
Earlier I’ve conceived an algebraic formula to characterize whether a quasi-uniform space is normal (where normality is defined in Taras Banakh sense, not in the sense of underlying topology being normal). That my formula was erroneous.
Today, I have proved another formula for this (hopefully now correct):
Theorem An endoreloid $latex f$ is normal iff $latex \mathsf{Compl} (\mathsf{FCD}) f^{- 1} \circ \mathsf{CoCompl} (\mathsf{FCD}) f \sqsubseteq \mathsf{CoCompl} (\mathsf{FCD}) f \circ (\mathsf{FCD}) f.$
The above formula also applies to any quasi-uniformity $latex f$.
The proof of the theorem is currently available in this PDF file.
Read my free ebook to understand formulas like this.
🔬 Advanced Mathematics References
- Sheaves in Geometry and Logic
- Categories for the Working Mathematician
- Stone Spaces
- Algebraic Topology (Hatcher)
- Concrete Mathematics
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From this formula it also follows that normality is determined by the underlying proximity and does not need particular uniformity.
Oh well, wrong. See my manuscript instead.