On D-connected sets in the space
Let be a continuum and a positive integer. Let be the hyperspace of all nonempty closed subsets of with at most components, endowed with the Hausdorff metric. For compact subset of , define the hyperspace . In this paper, we consider the hyperspace , which can be a tool to study the space . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility.
Let be a family of topological spaces and , for every . Suppose is the quotient space of the disjoint union of ’s by identifying ’s as one point . We try to characterize ideals of according to the same ideals of ’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let be an infinite cardinal. (1) Is there any ring and an ideal in such that is an irreducible intersection of prime ideals? (2) Is there...