Page "History of the separation axioms" Paragraph 7

In contrast, general topologists, led by John L. Kelley in 1955, usually did not assume T < sub > 1 </ sub >, so they studied the separation axioms in the greatest generality from the beginning.

Thus, they used the more complicated definitions for T < sub > i </ sub >, so that they would always have a nice property relating T < sub > i </ sub > to T < sub > j </ sub >.

Then, for the simpler definitions, they used words ( again, " regular " and " normal ").

Both conventions could be said to follow the " original " meanings ; the different meanings are the same for T < sub > 1 </ sub > spaces, which was the original context.

But the result was that different authors used the various terms in precisely opposite ways.

Adding to the confusion, some literature will observe a nice distinction between an axiom and the space that satisfies the axiom, so that a T < sub > 3 </ sub > space might need to satisfy the axioms T < sub > 3 </ sub > and T < sub > 0 </ sub > ( e. g., in the Encyclopedic Dictionary of Mathematics, 2nd ed.

).