On hereditarily decomposable hereditarily equivalent non-metric continua

HEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES 2XAND Cn(X)

Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...

Kernels of Hereditarily Unicoherent Continua and Absolute Retracts

For a hereditarily unicoherent continuum X, its kernel means the common part of all subcontinua of X that intersect all arc components of X. This concept naturally appears when absolute retracts for the class of hereditarily unicoherent continua are studied. Let Y be such an absolute retract. Among other results, we prove that (a) Y is indecomposable if and only if it is identical with its kern...

Optimal and Hereditarily Optimal Realizations of Metric Spaces

Hereditarily Optimal Realizations

Acknowledgments Obviously, though by no means trivially, many thanks are due to my advisor Professor Vincent Moulton, for introducing me to this fascinating subject, providing inspiration and helping me get started. Many thanks also to my colleague and co-author Dr. Katharina Huber for her patience during the many hours we spent going over the proofs in this paper. I am also most grateful to my...

Hereditarily effective typestreams

We prove that the hierarchy of hereditarily effective typestreams, that are effective models of inductivly defined types, has the length of the first recursivly inaccessible ordinal.