Abstract

Abstract Let 𝑋 be a non-metric continuum, and 𝐶(𝑋) be the hyperspace of subcontinua of 𝑋. It is known that there is no Whitney map on the hyperspace 2𝑋 for non-metric Hausdorff compact spaces 𝑋. On the other hand, there exist non-metric continua which admit and ones which do not admit a Whitney map for 𝐶(𝑋). In particular, a locally connected or a rimmetrizable continuum 𝑋 admits a Whitney map for 𝐶(𝑋) if and only if it is metrizable. In this paper we investigate the properties of continua 𝑋 which admit a Whitney map for 𝐶(𝑋) or for 𝐶2(𝑋).

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call