Homeomorphisms and Roman alphabet

Exercise:
"Which capital letters of the Roman alphabet are homeomorphic? Are any isometric?"

The only isometric ones I have found are N and Z. M and W could also be, if perfectly specular.
The real problem comes when I have to decide whether two letters are homeomorphic. I exploit the fact that the continuous image of a connected is connected. For instance, let's assume f:'A'->'B' is a homeomorphism. Any restriction of f is still a homeomorphism, but I can disconnect A by removing a point, while I need to remove at least two points from B to disconnect it. Then f cannot exist.
That was easy. But are A and P homeomorphic? No, wait, maybe I can say something like this: I can remove two points x,y from 'A' such that x and y have two non intersecting open neighborhoods and, by (bi)continuity, f(x) and f(y) should be apart, but there are no such points in 'P' whose removal would keep 'P' connected.
Then, I can bend a letter into another but without altering the "proximity" of its points. For instance I can't open an 'O' because I would alter the "proximity" of two points, and, dually, I can't link two point that were far apart.
Can anyone confirm these lucubrations?

Thank you in advance,
Kiuhnm
.

Relevant Pages

  • Re: Homeomorphisms and Roman alphabet
    ... Any restriction of f is still a homeomorphism, ... points from B to disconnect it. ... and y have two non intersecting open neighborhoods and, ... would alter the "proximity" of two points, and, dually, I can't link two ...
    (sci.math)
  • Re: Homeomorphisms and Roman alphabet
    ... Any restriction of f is still a homeomorphism, ... points from B to disconnect it. ... and y have two non intersecting open neighborhoods and, ... would alter the "proximity" of two points, and, dually, I can't link two ...
    (sci.math)
  • Re: Homeomorphisms and Roman alphabet
    ... Any restriction of f is still a homeomorphism, ... would alter the "proximity" of two points, and, dually, I can't link two ... the letter to be made of elastic solid (2 dimensional manifold), ... then they are both homeomorphic to a torus. ...
    (sci.math)