Subject: an old paper of Eilenberg?
From: "Ronnie Brown"
Date: Wed, 5 Jul 2006 11:33:34 +0100
I would be grateful for help in finding a reference, if I have remembered
it correctly! The background is as follows.
A paper on `Groupoids, the Phragmen-Brouwer Property, and the Jordan
Curve Theorem' (preprint 06.01 on
http://www.bangor.ac.uk/~mas010/brownpr.html).
has been accepted for JHRS subject to a few modifications, and the referee
reminds me that some results are kind of `known', but that the paper gives
short proofs.
One result used is that if X is the union of two path connected subspaces
whose intersection has n+1 components, then \pi_1(X,x) contains the free
group on n elements as a retract (with the usual local conditions). I now
recall that I saw this in a prewar paper of Eilenberg, in Fench I think.
But in contracting office due to retirement, the offprint got lost.
I canot find this on MathSciNet.
Can any one help? (I like to be accurate in historical matters, if
possible.)
Ronnie
www.bangor.ac.uk/r.brown