Irreducible continuum

A non-degenerate continuum that is irreducible between a certain pair of points, that is, does not contain any proper subcontinuum containing these points.

Comments

An example is the famous curve of $ \sin ( 1 / x ) $: it is the subset $ \{ 0 \} \times [ - 1 , 1 ] \cup \{ {( x, \sin ( 1 / x ) ) } : {0 < x \leq 1 } \} $ of the plane. This curve is irreducible between the points $ ( 0 , 0 ) $ and $ ( 1 , \sin 1 ) $.

References

[a1]	K. Kuratowski, "Topology" , 2 , Acad. Press (1968) (Translated from French)