From Algebraically Closed Fields to Indecomposable Continua
by
Paul Bankston
Marquette University

The classical technique by which one obtains algebraically closed field extensions; i.e., forming bigger and bigger fields by "throwing in roots of polynomials, " may be used to create unidimensional indecomposable continua: Start with any nondegenerate continuum X; take its bounded lattice of closed sets; ädd roots" in an iterated fashion; then apply the maximal spectrum. Result: A unidimensional indecomposable continuum Y, which one may take as having the same weight as X, plus a continuous surjection from Y to X. The main problem here is to get more information on the nature of continua constructed in this way.

Date received: January 15, 1998