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.

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- Feb 28th 2009, 10:19 AMhorowitzThe 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.

- Feb 28th 2009, 07:42 PMGammaBasis For RxR
The basis for the product topology is just the product of the basis of the individual topologies. So for $\displaystyle \mathbb{R}^2$ you just have elements of the form $\displaystyle (a,b) \times (c,d)$ for $\displaystyle a,b,c,d \in \mathbb{R}$. Think about what one of these looks like when you intersect it with X. That is your subspace topology.