
INGRAM COMMENT (modified):

 Figure A represents the first and second composite
of a mapping $f$ of a triod $T = OA \cup OB \cup OC$, onto
itself. The mapping $f$ has the property that $f(O) = B$,
$f(A) = C$, $f(B)= C$, $f(C) = C$, $f(C/2) = O$, $f(B/3)
=O$, $f(B/2) = A/2$, $f(2B/3)= O$, $f(A/4)= O$, $f(A/2) = A$, $f(3A/4) = O$
 and the mapping is piecewise
linear.  In the picture, the black square represents $O$,
the green arm is the image of $OA$, the blue arm is the
image of $OB$ and the red arm is the image of $OC$.  The
inverse limit of the inverse sequence, ${T,f}$, is an
atriodic tree-like continuum which is not chainable [Fund.
Math., 77(1972), 99
- 107].
We call it an \h{Ingram's Atriodic Continuum}.


If one imagines that the fat triod in the top of the Fgure A
represents the first of a sequence of tree chains covering
the inverse limit then the blue-green-red folded triod
represents the next terms of the sequence of covers.
