$\newcommand{\cl}{\mathrm{cl}}$ Let $X$ be a topological space and let $A_1,\ldots A_n\subset X$. Is it true that $$\cl\left(\bigcup_{m=1}^nA_m\right)=\bigcup_{m=1}^n\cl(A_m)$$ in an arbitrary topological space?
closure of finite unions
9
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general-topology
elementary-set-theory
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1Change the index $A_n$ to $A_m$ just to make the question mathematically perfect :-) – 2012-07-09
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0Fixed the index! :-) – 2012-07-09
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1Using `\operatorname{cl}` should give proper spacing (better than `\mathrm{cl}`. See [What's the difference between \mathrm and \operatorname?](http://tex.stackexchange.com/questions/48459/whats-the-difference-between-mathrm-and-operatorname) at TeX.SE. – 2012-07-11
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0Perhaps I should add to the previous comment that that's how it work in proper LaTeX. However most things work the same way in LaTeX and Mathjax. \\ On an unrelated note: I don't think that [tag:elementary-set-theory] tag fits here very good. – 2012-07-11