View source for Menger curve

An example of a curve containing the topological image of any curve (and, in addition, of every one-dimensional separable metrizable space). For this reason it is referred to as a universal curve. It was constructed by K. Menger [[#References|[1]]] (for Menger's construction see [[Line (curve)]]). The Menger curve is topologically characterized [[#References|[3]]] as a one-dimensional locally connected metrizable [[continuum]] $K$ without locally separating points (i.e. for every connected neighbourhood $O$ of any point $x \in K$ the set $O\setminus\{x\}$ is connected) and also without non-empty open subsets imbeddable in the plane.

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  K. Menger,   "Kurventheorie" , Teubner  (1932)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  A.S. Parkhomenko,   "What kind of curve is that?" , Moscow  (1954)  (In Russian)</TD></TR>
<TR><TD valign="top">[3]</TD> <TD valign="top">  R. Anderson,   "One-dimensional continuous curves and a homogeneity theorem"  ''Ann. of Math.'' , '''68'''  (1958)  pp. 1–16</TD></TR>
</table>

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