TITLE: Regular $T_2$ space which is not completely regular.
QUESTION [9 upvotes]: Theorem 10. of 
Pontryagin's Topological Groups says that:

Every Hausdorff topological group is completely regular.

But is there exists a Regular $T_2$ space which is not completely regular?

REPLY [4 votes]: These are counterexamples, which may be hepful for you:

Deleted Tychonoff Corkscrew
Hewitt’s Condensed Corkscrew
Thomas’s Corkscrew
Tychonoff Corkscrew