(adsbygoogle = window.adsbygoogle || []).push({}); 1. Hello, I'm reading through Munkres and I was doing this problem.

16.8) If L is a straight line in the plane, describe the topology L inherits as a subspace of ℝl × ℝ and as a subspace of ℝl × ℝl (where ℝl is the lower limit topology).

2. Relevant equations

3. The attempt at a solution

I've worked through it and seen many solutions online (they're all over). They essentially say that L, as a vertical line, inherits the standard topology on ℝ as a subspace of ℝl×ℝ, but some of the solutions jump from claiming that the basis sets in L are of the form {xo}×(c,d) for a vertical line L, which makes perfect sense, but then it jumps directly to saying that this implies that L inherits the standard topology, and I'm not sure I understand that (how can the topology of a 1-dimensional space be the topology on a 2-dimensional space?). Are the solutions maybe being informal, and instead mean that the topologies on L and R are "similar" (they are homeomorphic, but since homeomorphisms have not been introduced, we can't say this)?

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# Homework Help: Subspace Topology of a Straight Line

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