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Math notation for the closure of a set?

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Rui Maciel

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Mar 30, 2011, 11:35:11 AM3/30/11
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When I need to refer to the closure of a set I tend to use the \bar{}
command. So, considering the set \Omega then the closure of that set
would be:

\bar{\Omega}

Yet, I've noticed that when the symbol used to reference a given set also
has a superscript, the \bar{} doesn't look very good. I've also tried the
\overline{} instead but it appears even worse.

So, what's the standard way to represent the closure of a set with LaTeX?


Thanks in advance,
Rui Maciel

Enrico Gregorio

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Mar 30, 2011, 12:55:37 PM3/30/11
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Rui Maciel <rui.m...@gmail.com> wrote:

I'm usually satisfied with the result of \closure defined as
follows:

\newcommand{\closure}[2][3]{%
{}\mkern#1mu\overline{\mkern-#1mu#2}}

It takes an optional argument for fine tuning the offset of
the overline; the usual value is 3. Try

$\closure{\Omega}\closure[2]{\Omega}\closure[0]{\Omega}$

The last one should give the same result as \overline.

Ciao
Enrico

GL

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Mar 30, 2011, 12:07:19 PM3/30/11
to

For me the best is 0: \overline{\Omega} but
\overline{\Omega}\overline{\Omega} is the same as:
\overline{\Omega\Omega} which is not good ;-(

>
> Ciao
> Enrico

Rui Maciel

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Mar 30, 2011, 12:14:45 PM3/30/11
to
Enrico Gregorio wrote:

> I'm usually satisfied with the result of \closure defined as
> follows:
>
> \newcommand{\closure}[2][3]{%
> {}\mkern#1mu\overline{\mkern-#1mu#2}}
>
> It takes an optional argument for fine tuning the offset of
> the overline; the usual value is 3. Try
>
> $\closure{\Omega}\closure[2]{\Omega}\closure[0]{\Omega}$
>
> The last one should give the same result as \overline.

Thanks for the help, Enrico. It appears that your \closure{} command is
easier on the eyes than \bar{} and \overline{}. Nice. Kudos!


Rui Maciel

Enrico Gregorio

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Mar 30, 2011, 1:37:16 PM3/30/11
to
GL <goua...@gmail.com> wrote:

> Le 30/03/2011 18:55, Enrico Gregorio a ⁄crit :

The optional argument is precisely for this; if your
Omegas are upright, as is the default, probably the
best is [0], but try with \closure[0]{B} and \closure{B}
to see the real difference.

Ciao
Enrico

William F Hammond

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Apr 16, 2011, 7:02:13 PM4/16/11
to
Enrico Gregorio <Facile.d...@in.rete.it> writes:

> Rui Maciel <rui.m...@gmail.com> wrote:
>
>> When I need to refer to the closure of a set I tend to use the \bar{}
>> command. So, considering the set \Omega then the closure of that set
>> would be:
>>
>> \bar{\Omega}
>>
>> Yet, I've noticed that when the symbol used to reference a given set also
>> has a superscript, the \bar{} doesn't look very good. I've also tried the
>> \overline{} instead but it appears even worse.
>>
>> So, what's the standard way to represent the closure of a set with LaTeX?
>
> I'm usually satisfied with the result of \closure defined as
> follows:
>
> \newcommand{\closure}[2][3]{%
> {}\mkern#1mu\overline{\mkern-#1mu#2}}

I'm finding that


\newcommand{\closure}[2][3]{%

\overline{{}\mkern#1mu#2\mkern-#1mu}}
seems to work better. (I am using amsmath.)
For example, look at $\closure[N]{\Omega^*}$ for N in the
range -2 to 8.

-- Bill

Dan Luecking

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Apr 19, 2011, 3:04:47 PM4/19/11
to
On Sat, 16 Apr 2011 19:02:13 -0400, William F Hammond
<ham...@csc.albany.edu> wrote:

>Enrico Gregorio <Facile.d...@in.rete.it> writes:
>
>> Rui Maciel <rui.m...@gmail.com> wrote:
>>
>>> When I need to refer to the closure of a set I tend to use the \bar{}
>>> command. So, considering the set \Omega then the closure of that set
>>> would be:
>>>
>>> \bar{\Omega}
>>>
>>> Yet, I've noticed that when the symbol used to reference a given set also
>>> has a superscript, the \bar{} doesn't look very good. I've also tried the
>>> \overline{} instead but it appears even worse.

There is mathematical precedent for letting the closure of a set
be written with the bar _not_ covering the superscript:
\bar{\Omega}^*.
An alternative is to make the bar a superscript also:
(\Omega^*)\bar{\kern 5mu}

>>>
>>> So, what's the standard way to represent the closure of a set with LaTeX?
>>
>> I'm usually satisfied with the result of \closure defined as
>> follows:
>>
>> \newcommand{\closure}[2][3]{%
>> {}\mkern#1mu\overline{\mkern-#1mu#2}}
>
>I'm finding that
> \newcommand{\closure}[2][3]{%
> \overline{{}\mkern#1mu#2\mkern-#1mu}}

This second example has the effect of adding space to the
left of #2 and taking it away on the right. There should
be compensating \mkerns outside the \overline, as in the
first example.

It also shifts the bar left for positive values of #1,
where a slanted argument would want it shifted right and
an upright argument would not want any shift at all. I
would reverse the signs so that the most common cases
would have a positive argument (as in the first example).

Finally, the bar is almost always far to wide. I would
trim the size of the contents of \overline, as does the
first example.

I often use the following. Like the first example, it
shortens the bar, but makes the amount of shortening
independent of the amount of shift:

\def\closure#1#2#3{%
% #1 = amount to shift bar to right
% #2 = amount to shave off the ends of the bar.
% #3 = the symbol
\mkern#1mu\mkern#2mu
\overline{\mkern-#1mu \mkern-#2mu #3\mkern-#2mu \mkern#1mu}%
\mkern#2mu\mkern-#1mu}

Unfortunately, journals tend to ignore such niceties
and (if they use LaTeX at all) retype it themselves
using a plain \overline.


Dan
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