The homotopy equivalence classes of the sentence "I love the algebraic topology" 
Determine the homotopy equivalence classes of the sentence "I love the algebraic topology".

I want to learn that how we can define a homotopy on the set of letters of a sentence. Please with an example, explain this subject for me. Thank you.
 A: Two topological spaces $X$ and $Y$ are homotopy equivalent when there are functions $f:X\to Y$ and $g:Y\to X$ such that $g\circ f$ is homotopic to $\mathrm{id}_X$ (the identity function $\mathrm{id}_X:X\to X$) and $f\circ g$ is homotopic to $\mathrm{id}_Y$.
We can treat the letters of the alphabet as topological spaces. For example, the letter O can clearly be thought of as a circle. Similarly, the letter L is homeomorphic to an interval. The other letters can be identified with various combinations of circles and lines;  for example, B is like a circle joined to another circle at a point, since it has two "holes", and A is like a circle with two lines attached to it.
A "homotopy type" is just an equivalence class of topological spaces, where the equivalence relation is homotopy equivalence. In other words, two topological spaces are of the same homotopy type when they are homotopy equivalent. We might choose a simple representative of the equivalence class to refer to. So, we would often say 

The annulus has the homotopy type of the circle.

even though the sentence 

The circle has the homotopy type of the annulus.

is just as valid.
The question might be asking you to 

Take the letters occurring in the sentence, and identify which of them belong to which homotopy type

or it might be asking 

Take the entire sentence as a single topological space (i.e. as the disjoint union of its constituent letters), and identify the homotopy type of that space.

A: Here you have the alphabet according to homotopy types:

Here you have the alphabet according to homeomorphism:

Take your sentence I love the algebraic topology and identify the classes.
