What was the 'gold standard' textbook before Rudin? Furthermore, if anyone has knowledge of what textbooks Princeton or Harvard used back in the 1960's or 70's, I would highly appreciate it if you could tell me.
In the U.S. the two best known general topology texts from that period are probably John L. Kelley, General Topology ($1955$) and James Dugundji, Topology ($1966$). I was fortunate enough to learn topology from John Greever, using the final pre-publication version of his Theory and Examples of Point-Set Topology ($1967$), a modified Moore method text, but it was too idiosyncratic to attain wide popularity. Stephen Willard’s excellent General Topology came out in $1970$ and remains widely known, but it’s often considered to be at a slightly higher level.