On the definition of the relative topology on a subset of a topological space and with the weak topology defined by a function

A bump in the road in elementary topology

We observe a subtle and apparently generally unnoticed difficulty with thedefinition of the relative topology on a subset of a topological space, andwith the weak topology defined by a function.we observe a subtle and apparently generally unnoticed difficulty with thedefinition of the relative topology on a subset of a topological space, andwith the weak topology defined by a function.We observe a subtle and apparently generally unnoticed difficulty with thedefinition of the relative topology on a subset of a topological space, andwith the weak topology defined by a function.