A continuum $X$ is called *minimal* if it is not a single point and is homeomorphic to all its nontrivial subcontinua.
Here a trivial continuum is a single point.



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> What is an example of a minimal continuum not homeomorphic to the interval?
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This question is motivated by the following post and its related linked questions.


[Two consecutive continua](https://mathoverflow.net/questions/259017/two-consecutive-continua)



A minimal continuum
As Andreas points out in the comments, [the pseudo-arc](https://en.wikipedia.org/wiki/Pseudo-arc) provides an example of a continuum like this. This fact was first proved by Moise in 1948, in



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> Edwin Moise, "An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua," *Transactions of the AMS* **63** (1948), pp. 581-594.
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