double post.

No. Counters are fully enclosed.

I disagree. One talks of humanist typeforms having 'open counters' to maintain legibility at small sizes. This refers to letters like /a/, /c/, /e/ and /s/.

In metal typecutting, the matrix into which hot metal was forced was created by striking it with a steel punch. One way to get the right shaped punch was to use a 'counterpunch' to remove the insides of letters, even letters such as /H/ and /n/. So a counter originally would have been any white space removed from inside a letter.

I always thought of them as any space within a letter-form which is enclosed by three or more sides.

Well if they arent counters, what are they? Do they have a name? Is there a name for the highest dark shape shape in the last letter a in the original post?

Closed counters and open counters. I would consider a counter any white space that is visually internal to the letter shape as distinct from space between letters. Obviously in the case of open counters there is no hard line between counter space and inter-letter space, and the dynamic relationship of the two is an important aspect of type design.

Yes, it's an "open counter."