Examples of Strong Deformation Retracts

Question

I am new to topology and have come across strong deformation retracts.

I am aware that a certain spaces, such as a single point, a line, a disc, a plane all retract to a single point.

Similarly a cylinder to a circle.

Can someone confirm or correct my logic here:

if a shape can be 'molded' into another, such that no holes are created or removed, then a space can deformation retract to another. (Just like the famous mug and donut).

So in this case a torus could strong deformation retract to a circle, and a double torus to two circles joined at a point?

Also are there any other common examples I should be aware of?

Answer 1

All spaces $[0,1]^n, \Bbb R^n$, the Hilbert cube $Q = [0,1]^{\Bbb N}$ and more generally any compact convex subset with non-empty interior in a locally convex metric TVS, are examples of AR's.

In general, all AR's are contractible, which is quite obvious. I think they're all strong deformation retractible to a point (check Hu's book when in doubt).