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Message-ID:  <9704071439.AA03900@sgibulirsch6.mathematik.tu-muenchen.de>
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In-Reply-To:  <v02130500af6168f6317a@[130.237.37.44]> from "Hans Aberg" at Mar
              28, 97 02:14:32 pm
Date:         Mon, 7 Apr 1997 16:39:16 +0200
From: Johannes Kuester <kuester@MATHEMATIK.TU-MUENCHEN.DE>
Sender: Mailing list for the LaTeX3 project
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To: Multiple recipients of list LATEX-L
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Subject:      Re: rsfs
Status: R

>
> Johannes Kuester <kuester@MATHEMATIK.TU-MUENCHEN.DE> wrote:
>
> >May be there should be a fourth script-like font, or at least parts of
> >an alphabet in such a style, to be used for some special one letter symbols,
> >containing for example
> >
> >P for the power set (also mentioned in J. Ziegler's article)
> >C to denote the set of continuous / continuous differentiable functions
> >  (as in C^k(\mathbf{R}) or the like)
> >O and o for the Landau symbols (denoting the order of magnitude of
> >  a function)
>
>   I am thinking of having perhaps only two (using NFSS terminology)
> "scripty" families, one less scripty, like the AMSfonts Euler script, and
> one more scripty, looking like handwritten script, which would cover those
> symbols mentioned above, both upper/lowe case then. These families would
> then come in full (math) series (normal, bold) and shapes (upright,
> slanted).

(I suppose that `handwritten script' here refers to `Formal Script'
(e.g. rsfs fonts), is that correct?)

I'll try to be more explicit. One frequent notation of `power set'
is to use \mathfrak{P}. Now, if Fraktur is used for e.g. vector spaces,
this is ambiguous and should be avoided by escaping to \mathscr{P}.
But if Formal Script is used for another concept, one has to use
yet another symbol etc.
  Thus I think it would be better to have a special, reserved symbol
for `power set', clearly distinguishable from other `P's. Justin Zieglers
proposal contained a position for such a letter (and his article some
ASCII art to give an idea of that glyph), and WordPerfect has such a glyph
in (one of) its character set(s), though wrongly called `Weierstrass'
(no, it is not TeX's \wp for the Weierstrass `p' function, that glyph
is there, too (also called `Weierstrass').

Now there are more symbols with the similar problem: how to represent
them unambiguously. May be these won't make up a whole alphabet, may be
they shouldn't be called a font, as they need not share characteristics,
and may be they don't need to have a script-like appearance, but all this
doesn't change the mathematical necessity for such symbols, and I think
that TeX should provide them (may be after a lengthy discussion about their
appearance, as there does't seem to be a design for these symbols except
for the power-set-P).

Johannes Kuester

--
Johannes Kuester                    kuester@mathematik.tu-muenchen.de
Mathematisches Institut der
Technischen Universitaet Muenchen