📚 Recommended Mathematics Books
Topology (Munkres) | General Topology (Engelking) | Counterexamples in Topology | Rudin's AnalysisAs an Amazon associate, I earn from qualifying purchases.
I started research of mappings between endofuncoids and topological spaces.
Currently the draft is located in volume 2 draft of my online book.
I define mappings back and forth between endofuncoids and topologies.
The main result is a representation of an endofuncoid induced by a topological space.
The formula is $latex f\mapsto 1\sqcup\mathrm{Compl}\, f\sqcup(\mathrm{Compl}\, f)^2\sqcup \dots$.
However I proved this theorem only for the special case if every singleton is a closed set. Also the proof is not yet checked for errors.
🔬 Advanced Mathematics References
- Sheaves in Geometry and Logic
- Categories for the Working Mathematician
- Stone Spaces
- Algebraic Topology (Hatcher)
- Concrete Mathematics
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The proof was with a fatal error. I have removed the said theorem from my drafts. Instead I’ve added a counterexample.