Should there be a space in e.g./i.e. between a dot?

Should there be a space (thin space) in e.g./i.e. between a dot?

Taking in account that e.g. is shortening of exemplī grātiā, then one should use space between e.spaceg., is not it?

I believe that space should be thin, but it should be there no matter what. Or there is some other rule in english language?

No, there would be no space. When writing abbreviations that represent multiple words and that have periods appear within them, we don't put spaces after the internal periods.

Examples:

a.k.a. - also known as

d.b.a. - doing business as

e.t.a. - estimated time of arrival

There is not usually a space. Looking at these examples from the Oxford Dictionary you won't see spaces. In this context, the two word phrase is abbreviated to a single abbreviation, and is treated like a single word.