MathDB

We call a set

S

on the real line

\mathbb{R}

superinvariant if for any stretching

A

of the set by the transformation taking

x

to A(x) \equal{} x_0 \plus{} a(x \minus{} x_0), a > 0 there exists a translation

B,

B(x) \equal{} x\plus{}b, such that the images of

S

under

A

and

B

agree; i.e., for any

x \in S

there is a

y \in S

such that A(x) \equal{} B(y) and for any

t \in S

there is a

u \in S

such that B(t) \equal{} A(u). Determine all superinvariant sets.

Problem Statement