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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.

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    $\begingroup$ Why, out of curiosity? $\endgroup$ – user98602 Dec 1 '14 at 1:24
  • $\begingroup$ because many/most great mathematicians didn't use Rudin or Spivak, as these became popular after their education. That makes me curious. $\endgroup$ – minusatwelfth Dec 1 '14 at 1:35
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    $\begingroup$ Royden's Real Analysis was first published in the late 1960s and is one such option. It was based on his course at Stanford. We used it at my university at least into the 1990s. $\endgroup$ – Simon S Dec 1 '14 at 1:39
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    $\begingroup$ As I know by other people (old ones), it's Dieudonné's books on analysis. In Russia, they used those Shilov's book and other guy's book that now I cannot remember the name. $\endgroup$ – user40276 Dec 1 '14 at 2:36
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    $\begingroup$ Do you know that the year of publication of the first edition of Baby Rudin is 1953 ? $\endgroup$ – Tony Piccolo Dec 1 '14 at 7:56
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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.

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