DOI link for Inductive Limits
Inductive Limits book
The Dirac delta function δ which was 0 everywhere but 0 on R but still satisfied
∫∞ −∞ δ (t) dt = 1 served physicists and engineers well, although it
affronted and puzzled contemporary mathematicians. The comment of L. Schwartz [1966a, p. 3] is typical: “Les inge´nieurs 1’utilisent syste´matiquement, chacun avec sa conception personelle, avec la conscience plus ou moins tranquille.” It and its symbolic calculus relatives’ efficacy provoked mathematicians into probing the cause of the rumbling. The ultimate success of Sobolev  and Schwartz [1966a] undoubtedly provided smug comfort to some complacent engineers and physicists.