No abstract

No abstract

A decomposition of a topological space X is a partitioning of X into non-empty, disjoint sets called elements of the decomposition. An element of a decomposition is non-degenerate if it contains more than one point. Associated with each decomposition D of X is a topological space D*, called the hyperspace of the decomposition. A classical problem on decompositions of topological spaces is to find conditions under which D* is homeomorphic to X. Often decompositions arise from mappings: if g is a mapping of a space X onto a space Y, then D = {g-1(y) |y ∊ Y} is a decomposition of X.

No abstract