Which of the following set inequalities are true?

Asked Dec 23 '15 at 14:56

Active Dec 23 '15 at 18:49

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Let $G_1,G_2\subseteq \Bbb R^2$ .Let $f:\Bbb R^2\to \Bbb R^2$. Then which are correct?

I am getting $1,2$ as true. $3$ is false. If $W$ is open $x+W$ is open for all $x$. Thus $4$ is false. Are these correct?

edited Dec 23 '15 at 18:49

Martin Sleziak

asked Dec 23 '15 at 14:56

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1

That looks fine. – Lee Mosher Dec 23 '15 at 15:01
You might find some of such statements here. – Martin Sleziak Dec 23 '15 at 18:56
1 and 2 are true for any function with any domain or range. The simplest counter-example to 3 is to suppose that $G_i={x_i}$ for $i=1,2$ where $g_1\ne g_2$ but $f(g_1)=f(g_2)$. This also applies to functions in general.Note that 3 does hold when $f$ is 1-to-1. – DanielWainfleet Dec 23 '15 at 20:17
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I'm voting to close this question as off-topic because it contains multiple questions and has no content of lasting value. – Lord_Farin May 08 '16 at 09:43

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