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20cs700 [2020-09-09] – [Synopsis] Martin Ziegler | 20cs700 [2020-09-17] – [Synopsis] Martin Ziegler | ||
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**II. Computability theory over the Reals**: | **II. Computability theory over the Reals**: | ||
- | a) | + | a) |
- | b) Computing Real Sequences: semi-decidability / strong undecidability of equality, no computable sequence contains all computable reals \\ | + | b) Computing Real Sequences: semi-decidability / strong undecidability of equality, no computable sequence contains all computable reals |
- | c) Computing Real Functions: closure under composition and restriction and sequences, necessarily continuous, computable Weierstrass Theorem \\ | + | c) Computing Real Functions: closure under composition and restriction and sequences, necessarily continuous, computable Weierstrass Theorem |
- | d) | + | d) |
e) Multi-Functions & Enrichment: generalized restriction, | e) Multi-Functions & Enrichment: generalized restriction, | ||
f) Computing Real Operators: encoding continuous functions, encoding compact subsets \\ | f) Computing Real Operators: encoding continuous functions, encoding compact subsets \\ |