Timeline for Checking the uniform denseness of a set in $C([0, 1], \mathbb{R}^2)$

4 events

when toggle format	what		by	license	comment
Nov 11, 2020 at 2:50	comment	added	potionowner		Sure. I'll change the OP back and delete the comment. Thanks.
Nov 10, 2020 at 4:05	comment	added	Iosif Pinelis		@potionowner : Your original question was fully answered. If you actually meant to ask something else, you should now assume the responsibility for your original post (as for any other posts of yours) and post any other/further questions in separate posts. You should not change your question so as to invalidate a valid answer and nullify other people's time and effort (to help you, actually).
Nov 10, 2020 at 3:56	comment	added	Iosif Pinelis		@potionowner : the denseness of $S_2$ implies the denseness of $S_1$ because, whenever $S_2$ is dense (which never happens), $S_1$ is dense. Generally, implication $A\implies B$ holds (by definition) iff $A$ is false or $B$ is true. In particular, $A\implies B$ holds whenever $A$ is false (no matter whether $B$ is true or not). In our case, $A$ is the statement "$S_2$ is dense", which is always false. So, the statement "$S_2$ is dense" implies any statement whatsoever.
Nov 9, 2020 at 6:16	history	answered	Iosif Pinelis	CC BY-SA 4.0