CHAPTER XVIII - LOCALLY CONNECTED SPACES

Abstract

This chapter focuses on locally connected spaces. A topological space X is said to be locally connected at the point p if for each open set G containing p, p is an interior point of its component in G. The chapter describes the properties of locally connected spaces by presenting theorems that state that in a locally connected space every component C is an open set and that A space is locally connected if each component of an open set is open. The chapter also describes arcs and arcwise connectedness by presenting a proof of the theorem stating that if ab ∩bc = {b} 9, then the union ab ∪ bc is an arc ac.