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My question arises from a paper in the AMM (Rauch, 1978) in which the illumination problem is treated. The problem is given in an euclidean space, however Rauch uses terms that I think are from the topological figures —$\partial S$: Boundary?, $\bar{S}$: Closure?, etc— I don't sure about the definitions.

Sorry for the English mistakes Thank you!

dromastyx
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José Guzmán
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  • Related https://math.stackexchange.com/questions/2554698/example-of-a-vector-space-that-is-not-a-topological-space – Ethan Bolker Dec 12 '17 at 01:01
  • Those are topological terms. I suggest you look into an introductory textbook on general topology, preferably one which does $not$ begin with metric spaces. – DanielWainfleet Dec 12 '17 at 17:39

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Euclidean $n$-space is (most commonly) the space $\Bbb{R}^n$, with the dot product giving an inner product. This makes Euclidean $n$-space into an inner product space, which means it is a normed vector space, hence has a topological structure. In summary, a topological space is a huge generalisation of a Euclidean space, and all the notions from topology apply.

B. Mehta
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