Aposyndetic continua as bundle spaces

Abstract

Let S \mathcal {S} be the P P -adic solenoid bundle, and let η : X → S 1 \eta :X \to {S^1} be a map of the continuum X X onto S 1 {S^1} . The bundle space B B of the induced bundle η − 1 S {\eta ^{ - 1}}\mathcal {S} is investigated. Sufficient conditions are obtained for B B to be connected, to be aposyndetic, and to be homogeneous. Uncountably many aposyndetic, homogeneous, one-dimensional, nonlocally connected continua are constructed. Other classes of continua are placed into this framework.