NOTION FOR CONNECTEDNESS AND PATH CONNECTEDNESS IN SOME TYPE OF TOPOLOGICAL SPACES

Abstract

The notions of connectivity and path connectivity of topological spaces in the part of general topology are firmly related. In particular, path connectivity is a tougher condition of connectedness and reversal does not always apply. When it comes to metric space, the notion of connectedness is more difficult to formulate precisely, while the path connectedness is a concept whose definition remains the same and easier to understand in these spaces. In this text, there are examples of connectedness, path-connectedness and simultaneously connected and path-connected topological spaces. Also, an additional condition is required for which the relation of the connected space is valid to be followed by a path connected.