1. ## The subspace topology

Let X={(x,0) ∈R^2|x ∈R}, the x-axis in the plane. Describe the topology that X inherits as a subspace of R^2 with the standard topology.

2. ## Basis For RxR

The basis for the product topology is just the product of the basis of the individual topologies. So for $\mathbb{R}^2$ you just have elements of the form $(a,b) \times (c,d)$ for $a,b,c,d \in \mathbb{R}$. Think about what one of these looks like when you intersect it with X. That is your subspace topology.