13
$\begingroup$

A space $(X,\tau)$ is called rigid if $\textrm{Aut}(X)=\{\textrm{id}_X\}$. We say $(X,\tau)$ is strongly rigid if for every continuous map $f:X\to X$ we have that $f = \textrm{id}_X$ or $f$ is constant (that is there is $x_0\in X$ such that $f(x)=x_0$ for all $x\in X$).

Is there a strongly rigid Hausdorff space with more than 1 element?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
17
$\begingroup$

Yes, see for example "Continua which admit only the identity mapping onto non-degenerate subcontinua" by H. Cook (Fund. Math. 60, 1967, 241-249).

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .