Prove that $E$ is a connected subset of $R^2$

Question

Let $E\subset R^2$ be the collection of all points such that at least one of their coordinates is rational, Prove that $E$ is a connected.

Even though the question has been answered, please show some work next time =] — LASV, Dec 02 '13 at 06:54

score 1 · Answer 1 · edited Apr 13 '17 at 12:21

1

Each point connects to the x or y axis which connects to the origin, so the collection is connected.

Edit: here is a related question discussing connectedness vs. path connectedness and methods of proof

edited Apr 13 '17 at 12:21

Community

answered Dec 02 '13 at 06:32

comptuerbro

Aren't you thinking of path connected? Note however, that path connected does indeed imply connected. – mathematics2x2life Dec 02 '13 at 06:36
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path connected implies connected – comptuerbro Dec 02 '13 at 06:39
@comptuerbro Could you please elaborate a bit more? I still don't understand how you proved that E is path connected. – LPS Dec 02 '13 at 07:55

1 Answers1