Talk:Euclidean topology

I'm reading out of a book that calls the set of all interiors of circles in a plane the basis of the Euclidean Topology for the plane. The Euclidean Topology for the plane wasn't mentioned in this article. The book is called Topology by John G. Hocking and Gail S. Young. Bpsuntrup (talk) 00:14, 26 July 2011 (UTC)

Distinction between Euclidean topology and Euclidean space
I do not recommend merging Euclidean topology with Euclidean space. The latter term is highly loaded: while Euclidean space usually refers to the topological space $$\mathbb R^n$$, the term "Euclidean space" usually incorporates some particular structure, like the Euclidean inner product, the Euclidean metric, or the Euclidean group. The concept of Euclidean topology refers strictly to the topological structure of $$\mathbb R^n$$, which is of course intimately related with the algebraic structures of Euclidean space, but is conceptually distinct from them. --Hierarchivist (talk) 02:23, 26 May 2013 (UTC)

Generalization
Just noting that I cut out some extraneous information relating to definition of a topology, since the page read like the notes of a novice student, and also generalized the idea from R to R^n. Quiddital (talk) 20:59, 4 June 2016 (UTC)