 The space "X" is said to be weakly locally connected if it is weakly locally connected at "x" for all "x" in "X".In other words, the only difference between the two definitions is that for local connectedness at "x" we require a neighborhood base of "open" connected sets containing "x", whereas for weak local connectedness at "x" we require only a neighborhood base of connected sets containing "x".Evidently a space that is locally connected at "x" is weakly locally connected at "x".