"E.g." or "e. g." (with a blank)?

Solution 1:

A lot depends on which scientific field you're talking about. The style sheets for the Linguistic Society of America and the American Psychological Association, for instance, could hardly be more different.

Me, I always use e.g, ending with a comma or occasionally a colon if it's followed, as usual, by a list of examples. No space necessary, though if you're into beautiful formatting, I agree a thinspace is nice. But the editor will do that automatically if you're publishing on paper, and if they care about typographical beauty. Quite often they don't.

There's no standard on punctuation or typography. Individual rags have individual policies, but if you're not getting paid to follow them, there's no reason to pay them any attention, unless you personally find them agreeable rules to follow.

Especially for scientific papers. In the US, scientists are not expected to be able to write English very well, and that expectation is quite often fulfilled. So there are always editors, many of whom are competent.

Solution 2:

Spaces between multiple word abbreviations are usually dropped - see Wikipedia's entry on e.g.. There are plenty of other examples, such as "S.W.A.T.", though sometimes the full stops are dropped altogether, as in "USA" or "UK".