TITLE: Regular spaces that are not completely regular
QUESTION [14 upvotes]: In the undergraduate toplogy course we were given examples of spaces that are $T_i$ but not $T_{i+1}$ for $i=0,\ldots,4$. However, no example of a space which is $T_3$ but not $T_{3.5}$ was given. Later I was told by a colleague that such examples are rare and difficult to construct.
I know there is an example of such a space, called the Tychonoff corkscrew (or the spiral staircase), in the "Counterexamples in topology" book by Steen and Seebach. I've also found the following paper, though at the moment I'm not able to view it: A.B. Raha "An example of a regular space that is not completely regular", Proceedings Mathematical Sciences 102 (1992), 49-51.
Are there any other, folklore examples of regular spaces that are not completely regular? Are there any relatively easy ones?

REPLY [2 votes]: In the "Handbook of the History of General Topology" vol. 1, M. E. Rudin in the article "The early Work of F. B. Jones", commenting the results of F. B. Jones introduced the name  "The Jones machine". The Jones machine is a simple design which, using countably many copies of a completely regular space, but not normal, creates a regular space, but not a completely regular one.
   In the article "On regular but not completely regular spaces", Topology and its Applications
Volume 252, 1 February 2019, Pages 191-197, we give a simple, i.e., available for ordinary students of mathematics, examples of applying this method.