DefinitionConnectedness and separation axioms are properties of topological spaces, which all define relationships between open sets in topological spaces based on their geometric structure. Connectivity states that a space cannot be covered by two disconnected open sets, Separation properties encode the idea that it should be possible to separate points and sets in certain ways with open sets. In topology, such concepts are basic to defining and understanding spaces, as well as being used for properties like continuity, compactness and convergence. Example: The number line for real numbers is all connected, meaning that any 2 points, regardless how far away they are, can be connected by a path within this space. Furthermore, the real line is an Hausdorff space, i.e.: the space is separated, meaning, that each two points have disjoint neighborhoods.
