View source for Irreducible continuum

<!--
i0525801.png
$#A+1 = 4 n = 0
$#C+1 = 4 : ~/encyclopedia/old_files/data/I052/I.0502580 Irreducible continuum
Automatically converted into TeX, above some diagnostics.
Please remove this comment and the {{TEX|auto}} line below,
if TeX found to be correct.
-->

{{TEX|auto}}
{{TEX|done}}

A non-degenerate [[Continuum|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====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  K. Kuratowski,   "Topology" , '''2''' , Acad. Press  (1968)  (Translated from French)</TD></TR></table>