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Results tagged with transfinite-induction
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user 161756
1
vote
0
answers
180
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Partition $\mathfrak c$-dense set to $\mathfrak c$- many dense set
A subset of $A\subset\mathbb R$ is called $\mathfrak c$-dense if $ |A\cap I|=\mathfrak c$ for any none open interval $I\subset\mathbb R.$ Then, there is a partition for $A$ to continuum many dense s …
- 179
4
votes
0
answers
175
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Construction of a function by transfinite recursion
Let $\mathcal F:=\{f_\xi\colon \xi<\mathfrak c\}$ be a family of functions from $\Bbb R$ to $\Bbb R$ and $K$ be a nonempty perfect set. The question is
Construct a function $g\colon \Bbb R \to \Bbb R …
- 179