Covering dimension of inverse limit of fuzzy spaces
In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If is a perfect subparacompact space and is a countable collection of subparacompact Čech-scattered spaces, then the product is subparacompact and (2) If is a countable collection of metacompact Čech-scattered spaces, then the product is metacompact.
Let X denote a locally connected continuum such that cyclic elements have metrizable boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.