I always stumble when using abbreviations in a sentence, as they inherently contain a period in them. How do I use a comma or a semicolon after an abbreviation? How about a period?
E.g. (This is an example of my quandary)
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Based on the "Oxford Manual of Style" I changed my approach:
But, when I was reading Mathematics at university I was told to always add the sentence ending period whatever went before, so if an equation ended with ellipsis there would be four periods together.
Summary: it is a matter of style.
This pretty much explains who the period belongs to:
This one is simple enough: never double up periods. If a statement ends with “etc.” the period in the abbreviation does double duty, serving as the full stop to end the sentence. If, however, you need another mark of punctuation after an abbreviation, you can put it after the period
So, it really belongs to no one: it is shared. Your link would include the period.
N.B., emphasis added by me.
To ensure that there is only one period; taken from Wikipedia:
Abbreviations A full stop is used after some abbreviations. If the abbreviation ends a declaratory sentence there is no additional full stop immediately following the full stop that ends the abbreviation (e.g., My name is Gabriel Gama, Jr.) This is called haplography. Logically there should be two full stops (one for the abbreviation, one for the sentence ending), but only one is conventionally written. In the case of an interrogative or exclamatory sentence ending with an abbreviation, a question or exclamation mark can still be added (e.g., Are you Gabriel Gama, Jr.?). 
I would go with the "clarity rule," use the punctuation that makes the most sense and makes your meaning easiest to discern.
In practice I try to structure my sentences to avoid having to place an abbreviation at the end, where the closing period would collide with the full stop at the end of the sentence, but otherwise use the periods and punctuate the rest of the sentence as required; if the sentence structure requires a comma or semi-colon after the abbreviation then I would place it after the period.
You could avoid the problem by removing the periods (or full stops). Eg: like so. In fact, the B.B.C. has completely done away with periods in abbreviations and acronyms in its writing, as have several other publications. If you do decide to include periods within your writing, you can simply place the punctuation directly after them, unless it is a period. For instance, an abbreviation for doctor is Dr. This sentence is a new sentence, but if I was talking about a Dr. and didn't have a capital letter, it is quite obvious that it is the same sentence.
So you have at least two choices:
p.s. E.g. (exempli gratia) is also an acronym.
When you end a sentence with an abbreviation, you don't need an extra period. The story is different when the sentence is a question or exclamation—then you need both punctuation marks.