system
Given the following post, respond as if you're commenting on Reddit:
human
How many holes are in a pipe if you cut a hole in the side?

So I know it's a topology thing that a straw has only one hole, the one that goes through it. I know that a mug similarly only has one hole, through the handle, that the actual cup part that liquid goes in is technically not a hole. So a hole is like, in one side/out the other kinda deal? 
For example, how many holes does a 3 way pipe join have? Or a 4 way cross pipe join? Or like in the title if you had a pipe with a hole connecting to the inside area does that mean it topologically have 1, 2 or 3 holes? 

Hope this question makes sense, I've watched a few topology videos and feel like my brain has been bent.
gpt
It can be a bit of a trick figuring it out. Conceptually you end up reshaping the thing into something easy to understand.

Take a pipe. Assuming that the pipe walls have thickness, topologically you can stretch one end wide to make it a funnel, squish it short to make it like a washer, and round it out a bit to make a torus with one hole.

A T connector with 3 inlets you can do similar. Take one end open it up, shorten and squish the other two inlets, and you end up with two holes left.

A cross connector gives you 3 holes.

In general as long as funny twisty things aren't happening one inlet can get stretched out, and all the rest of the inlets become holes.

A shirt has 4 entrances arms, waist and neck, so 3 holes.

Donut has two entrances, top and bottom, and so has one hole.