View source for Indecomposable continuum

{{TEX|done}}
A non-degenerate [[Continuum|continuum]] that cannot be represented as the union of two proper subcontinua.



====Comments====
Two equivalent definitions: 1) there are three points such that the continuum is irreducible between each pair of points from these three (cf. [[Irreducible continuum|Irreducible continuum]]); and 2) every proper subcontinuum is nowhere-dense.

In indecomposable continua one has composants, which are like components: the composant of a point $x$ is the union of all proper subcontinua containing $x$.

Examples of indecomposable continua are the [[Pseudo-arc|pseudo-arc]], which is even a [[Hereditarily indecomposable continuum|hereditarily indecomposable continuum]]; a [[Solenoid|solenoid]]; and the remainder $\beta\mathcal{H} \setminus \mathcal{H}$ in the [[Stone–Čech compactification|Stone–Čech compactification]] of the half-line $\mathcal{H} = [0,\infty)$.

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  D.P. Bellamy,   "A non-metric indecomposable continuum"  ''Duke Math. J.'' , '''38'''  (1971)  pp. 15–20</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  K. Kuratowski,   "Topology" , '''2''' , Acad. Press  (1968)  (Translated from French)</TD></TR>
</table>