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Wikipedia defines counter then gives examples.
Then it proceeds to give examples of open counter without having given any definition of it:

In typography, a counter or aperture is the area of typeface anatomy that is entirely or partially enclosed by a letter form or a symbol (the counter-space/the hole of). Letters containing closed counters include A, B, D, O, P, Q, R, a, b, d, e, g, o, p, and q. Letters containing open counters include c, f, h, i, s etc.

So, what is the proper definition of "open counter"?
To illustrate, could you give a handful examples of characters that contain no open counters?

Is it synonymous with "aperture"? 'Fonts and Encodings', O'Reilly 2007. Pg. 4 says:

The counter, which is the inner part of a letter, for example, the space inside an 'o' and 'O', a 'D', etc. The counter of an 'e' is commonly called an eye. When the letter is open at one end, as is the case with 'n' we speak instead of an aperture.

I have drawn my interpretation of open counter in green below, is it correct?

enter image description here

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2 Answers 2

Using a map metaphor:

A counter is a lake.

An open counter is a bay.

enter image description here

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So there are not so many examples of characters that contain no open counters I guess? Except 0 o 。. ・ - _ \ / ` | ' –  Nicolas Raoul Apr 17 at 1:04
    
Correct. Actually, I'm not entirely sure what wikipedia considers the open counter in an 'i' to be. Remember that type terminology tends to be a little fuzzy in nature. The definitions are more along the lines of 'mostly accepted conventions' but there's always room for debate. –  DA01 Apr 17 at 1:06
    
I'd think an i can have an open counter if it curves towards the bottom-right. But it's an uneducated guess. –  Yisela Apr 17 at 2:06

Adding to DA's great answer, some more info about open counters and legibility.

First of all, as mentioned a counter is the partially (open) or fully (closed) enclosed space in a letter. As I see it, all these letters have counters: b,d,g,o,p,q,A,B,D,O,P,Q and R. An these have open counters: a,c,g,s,C,G and S.

Another example of an open counter to add to the 'cartography a":

enter image description here

Source

Counters can help with legibility, although they need to be combined with other properties such as x-height:

Taller x-heights (usually) result in an overall increase in legibility, thus causing a direct correlation between counters and x-height.

Compare the difference between a typeface with small short counters and a typeface with large counters and taller x-height:

enter image description here

While the first one has large counters, the second one has smaller ones, but larger x-height. Of course larger x-heights is just part of the equation. The most efficient typefaces with the best ratio of x-height and cap height seem to be between 67 to 69 percent of the cap height.

A nice related article on legibility and the related study where the previous information came from.

Source

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So, small counters can imply legibility, and small counters imply large open counters, right? In the image, is it intended that the blue zone does not reach a bit further right? This image invalidates the definition I was thinking about, which was "every point that is not part of the letter but can be reached by drawing a line between two points belonging to the letter". –  Nicolas Raoul Apr 17 at 2:14
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@NicolasRaoul I don't think such hard math-based rules will work well with typographic definitions. Again, we're a bit loose with our terms and definitions in the world of type. –  DA01 Apr 17 at 2:15
    
I have to agree. I had a more flexible concept of open counter in mind, you last example made it trickier for me. I wouldn't consider those spaces as structural parts of the glyph, but I like to think of a and e as good examples of open counters. –  Yisela Apr 17 at 2:30

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