In a unit square, if there are uncountably many points S, is there a line with infinitely many points of S on it? – math.stackexchange.com

In a unit square, if there are uncountably many points S, is there a line with infinitely many points of S on it? – math.stackexchange.com

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If not, how many points can be guaranteed? Also, I'm not sure about my tag. This is a pretty general question. I figured General Topology is close. EDIT: Someone paraphrased this nicely. "Let $S\...

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