# Why does the letter $X$ deformation retract onto a point? (Hatcher's Algebraic Topology, Chapter 0, pg 2)

I am stumble at a statement from Hatcher's Algebraic Topology Chapter 0 at Page 2 which can be found here.

The thick $\mathbf{X}$ deformation retracts to the thin $X$, which in turn deformation retracts to the point of intersection of its two crossbars. The net result is a deformation retraction of X onto a point, during which certain pairs of points follow paths that merge before reaching their final destination.

So what "two crossbars" mean here? Why $X$ retracted onto a point? And where certain pairs of points merge? Thank you very much.

## 1 Answer

The crossbars are \ and /. Imagine each of the two crossbars shrinking towards the point at which they cross at the centre of X.

• That's great, thanks Michael. – 1LiterTears Aug 28 '13 at 3:10