Date of Award
Doctor of Philosophy (PhD)
Eberhart, Nadler, and Nowell asked for which Peano continua X is it true that (GAMMA)(X), the space of order arcs in C(X), is homeomorphic to the Hilbert cube ? They answered the question affirmatively when X contains no free arcs. In Chapter IV, we characterize those 1-dimensional ANR('s) X for which (GAMMA)(X) is homeomorphic to . In Chapters I and II, we develop techniques for analyzing this problem and, in Chapter III, we also apply these techniques in answering some open questions concerning Whitney levels in C(X).
Lynch, Mark James, "Spaces of Order Arcs in Hyperspaces of Subcontinua." (1985). LSU Historical Dissertations and Theses. 4099.