Aposyndetic Continua as Bundle Spaces

Abstract

Let $\mathcal {S}$ be the $P$-adic solenoid bundle, and let $\eta :X \to {S^1}$ be a map of the continuum $X$ onto ${S^1}$. The bundle space $B$ of the induced bundle ${\eta ^{ - 1}}\mathcal {S}$ is investigated. Sufficient conditions are obtained for $B$ 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.