# What's right topology for a concave polygon?

I have a problem with the topology of a concave corner in a text I have traced. The corner must be sharp so I placed some proximity edges to avoid the subsurf modifier smoothing.

This is how I managed a convex area. I don't know if the topology is correct, but I don't have any problem:

I tryed something similar in a concave area, cutting through one more loop:

When the subsurf is applied, the result is really bad. It seems like there is a hole somewhere, or some rogue faces, but it's not. Everything is "ok".

I can't understand why this happens. It's even all quads. There is clearly something I don't understand, so I hope to receive some help.