The way I was taught when I was learning to type was that it depended on the form of punctuation you were using.

If you were using 'closed punctuation' (considered old-fashioned)you would put a full stop after every abbreviation and initial, so...
Dr. A. N. Other

And when writing you would not leave a clear line between paragraphs, but would instead indent the first line of the paragraph by five spaces (1 tab stop).

This produced a fairly dense, cluttered page of type.

In 'open punctuation' you omitted full stops for abbreviations and initials...
Dr A N Other

and simply left a clear line between paragraphs instead of indenting the first line.

This produced a much cleaner page of type that was easier on the eye.