Abstract
This chapter discusses some questions from topology that may seem in and out of context. Some of them are just isolated questions that may not lead anywhere; some are missing links in different developments. The first conjecture discussed in the chapter is: “Let X be a tree-like continuum and let f: X →X be a continuous map. Then there exists an indecomposable continuum W ⊆X such that f(W) ∩ W ≠ ϕ.” Second conjecture discussed was posed by Norman Passmore, in his Ph.D. dissertation in 1976, and is still open. It states: “Let P be a pseudo-arc and let C(P) denote its hyperspace of sub-continua. Let X ⊆C(P) be a pseudo-arc. Then X is a subset of a Whitney level for some Whitney map μ.” Third conjecture discussed was posed by Howard Cook and states: “Let A ⊆ℝn be a compact set with the property that every component of A is either a point or a pseudo-arc. Then there exists a pseudo-arc P with A ⊆P ⊂ℝn.” Various other conjectures and problems are also solved.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have