In Swedish, it's common to replace the periods with spaces when using an abbreviation. Is this valid in English? Personally, I think this approach is easier to use and looks better in text (and all problems with multiple periods magically disappear). Of course, it doesn't work in all situations, but still.
Some examples to further illustrate my question:
That's a car, i e you can drive it.
There are many things you cannot do, e g carry a gun on a public street.
What is that? It's a p v t!
I made the last one up, by the way, if someone didn't notice.
Best Answer
Sigh. There are no easy answers, as my numerous edits would attest had you been with me whilst writing an answer.
Ultimately the form of such abbreviations, initializations, and acronyms are determined by common usage (whether it be informal or formal) and style guides (e.g., newspapers, journals, magazines, etc.), and one will almost always find an exception to any "prescribed rule".
Just look at these examples to see what I mean (from an American English perspective):
Units and time get no love either:
Acronyms can vary widely:
Not even people get respect all the time:
One thing is nearly universal, however: if the period is omitted, the letters are written without intervening spaces. It would be extremely rare to see e g, i e, N A S A, D r, a m, A S A P. If spaces are used, it is usually in conjunction with the period: A. M., e. g., i. e., A. S. A. P.
There is, unfortunately, no one rule that fits every case where a word or phrase is shortened; the only real option is to follow common usage, or the style guide if one is present.