Double Buckethandle

The Cantor 1/5-discontinuum C₅ is created using the procedure of deleting the second and the fourth segments from five equal segments (instead of the middle third for the Cantor Ternary Set). C₅ is the set of the reals in the unit interval which can be represented without 1-s and 3-s in the form

$$\sum _{n=1} ^\infty \frac{a_n}{5^n} \quad .$$

The Double Buckethandle continuum is the union of: (i) the half circles in the lower plane going through points of $C_5 \cap \{x : 2/5^{n+1} \le x \le 1/5^n\}$ with the centre $7/10\cdot 5^n$, (ii) the half circles in the upper plane going through points of $C_5 \cap \{x : 2/5^{n+1} \le 1-x \le 1/5^n\}$ with the centre $1-7/10\cdot 5^n$.

We can find more in [55, p.205 - p.206].

Double Buckethandle - fig. a


Double Buckethandle - fig. b


Source files: a.eps . a.gif . b.eps . b.gif . example.htm . figure.mws . figureb.mws . latex.tex . title.txt .

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