Chapter 5 Normed Spaces and Their Topology (part II)
In order to see the real import of continuity, we need to introduce some additional properties a set might or might not have. These are significantly more complicated than the definitions of open and closed, which involve three nested quantifiers (\(\forall\exists\forall\)). So we will have to pay very close attention to the quantifiers and how we might blueprint proofs involving these new notions.
