Span And Semispan Of Metric Continua
Date of Award
Doctor of Philosophy (Ph.D.)
R. H. Bing proved that the monotone image of a chainable continuum is a chainable continuum and Rosenholtz showed that the open image of a chainable continuum is chainable. These results are extended to circularly chainable continua, and we show that the monotone image of a space with span or semispan zero has span or semispan zero. Ingram showed that the unicoherent atriodic union of two chainable continua is chainable and Fugate characterized chainable continua in terms of their indecomposable subcontinua. We show that the unicoherent atriodic union of two spaces with semispan zero has semispan zero and characterize semispan zero in terms of subcontinua which may be slightly different from indecomposable subcontinua. Several theorems which describe when span zero and semispan zero are equivalent are presented.
Kell, James Alva Iii., "Span And Semispan Of Metric Continua" (1980). Dissertations from ProQuest. 1145.