My friend told me that $b \simeq o$ topologically.

Question

My friend told me that for two letters $b,o$ of the alphabet, we have that $b \simeq o$ topologically.

But I don't have any knowledge of topology. Can you recommend a text to understand (as fast as possible) the above statement?

Thank you.

Answer 1

They are not homeomorphic, however b deformation retracts on o (which roughly means that you can suck the antenna of the b back along itself till it disappears), and therefore any relevant invariant from algebraic topology will tell you that b and o are the same from its point of view. They are said to have the same homotopy type.

Answer 2

They are not homeomorphic because if such homeomorphic exist say f, then if you remove the mid point of top antenna of “b”, it would have two connected component but removing any point from the letter “o” would still give a connected set. So such f can not exist.

Answer 3

What is your definition of a bee or an oh? The bee and the oh on the left in the following figure are homeomorphic, in other words: topologically the same; but the bee and the oh on the right are not homeomorphic: All small pieces of the oh are just little intervals, but the bee has two "special points".