How to properly read this proposition?

Asked Nov 08 '20 at 18:31

Active Nov 08 '20 at 18:36

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I'm reading this book (OK, Efe A. Real analysis with economic applications. Princeton University Press, 2007.) and in page 143 the author claim this proposition:

I don't know how to properly read the part after the equal sign of U, can someone rephrase it in other words?

edited Nov 08 '20 at 18:36

asked Nov 08 '20 at 18:31

Bruno Ruas

2

"$U$ is the union of all the elements of $\mathcal{O}$ contained in $U$". – TheSilverDoe Nov 08 '20 at 18:33
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There is no definition of $U$. $U$ is just some arbitrary open subset of $X$, and according to this proposition, we can find some countable class $\mathcal O$ satisfying the statement given above. – player3236 Nov 08 '20 at 18:35
how U can be the union of elements contained in itself? it is not redundant? – Bruno Ruas Nov 08 '20 at 18:38
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Does this answer your question? Unclear use of big union symbol in proof of a fixed point theorem – Mark S. Nov 08 '20 at 18:39
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It looks like the proposition is saying that each open set in $X$ is a union of sets belonging to $\mathscr{O}$. – Barry Cipra Nov 08 '20 at 18:44
i think that's the way of read it, Barry Cipra! something like "every subset O of U belongs to O' too" – Bruno Ruas Nov 08 '20 at 19:01
Barry Cipra's comment is correct, but what Barry Cipra said is very different from "every subset O of U belongs to O' too" – Mark S. Nov 08 '20 at 21:57

How to properly read this proposition?

0 Answers0