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Results tagged with real-analysis
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user 517040
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
9
votes
Extracting a common convergent indexing from an uncountable family of sequences
We prove that $\mathbb c=\mathbb c_{\mathbb R}$: clearly $\mathbb c\le\mathbb c_{\mathbb R}$ holds, hence it is enough to prove $\mathbb c\ge\mathbb c_{\mathbb R}$. This means: for all reflexive separ …
- 300
11
votes
Extracting a common convergent indexing from an uncountable family of sequences
Using notation by the answer by Hamkins, I'll prove that $\mathbb c_{\mathbb R}\ge\min\{\mathfrak s,\mathfrak b\}$.
Thanks to Theorem 8.11 of Halbeisen's book Combinatorial Set Theory, we know that $\ …
- 300