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I recently started reading Topology and Groupoids by Ronald Brown and this notation came up. The notations is $$[x,\to[ \; =\{z \mid x \leq z\}$$ and a similar notation for other type of intervals. I have never seen this before, and I was baffled wondering if this was a funny $\LaTeX$ macro mistake where "2" was used as "\to" in some situations. I am wondering if it is sort of common? Is it common in some area of mathematics? If it is not clear, I am asking about using the "$\to$" arrow not really the brackets (although I rarely see the bracket notation).

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@AndresCaicedo Thanks. I was thinking when I figured out the notation that it was less deceptive than the $+\infty$ and $-\infty$ notation. Although it looks funny when writing functions with these arrow intervals, I guess no notation is perfect. You should post your comments as an answer. – Paul Plummer Jun 23 '13 at 18:47
up vote 5 down vote accepted

It is not uncommon.

When discussing (partially) ordered sets, people sometimes use $\leftarrow$ and $\to$ rather than $-\infty$ and $+\infty$, so the interval $(\leftarrow,b)$ means the same as what other times one writes as $(−∞,b)$, that is, $\{z\mid z<b\}$. The use of $],[$ is also common enough (and dates back to Bourbaki), with $]a,b[$ meaning the same as $(a,b)$, etc.

Here are some examples: 1, 2.

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