On continuous images of ultra-arcs.

Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight ≤ ℵ 1 is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present. • Every nondegenerate locally connected chainable continuum of weight ≤ ℵ 1 is a co-elementary monotone image of any ultra-arc. • Every nondegenerate chainable metric continuum is a co-existential image of any ultra-arc. • Every chainable continuum of weight ℵ 1 is a co-existential image of any ultra-arc whose indexing ultrafilter is a Fubini product of two free ultrafilters. • There is a family of continuum-many topologically distinct nonchainable metric continua, each of which is a co-existential image of any ultra-arc. • A nondegenerate continuum which is either a monotone or a co-existential image of an ultra-arc cannot be aposyndetic–let alone locally connected–without being a generalized arc. [ABSTRACT FROM AUTHOR]