self-maps

spaces/S000151/properties/P000138.md

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+---
+space: S000151
+property: P000138
+value: false
+---
+
+For every irrational $\theta\in[0,1]$ there exists
+a contiunuous self-map of $X$ such that its set
+of fixed points is exactly $[0,\theta)\cap\mathbb Q$.
+
+The construction of a map $(\theta,1]\cap X \to (\theta,1]\cap X$ with no fixed point is analogous as in the proof that
+{S150|P89}
+(use only the sequence $b_k$).