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Math Help - The subspace topology

  1. #1
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    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.
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  2. #2
    Super Member Gamma's Avatar
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    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.
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