Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topological topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 22nd 2010

    Just got the following query from Harald Hanche-Olsen about the page separation axioms. As I’ve never seen that notation before either (but agree with Harald’s comments in both parts), I’m forwarding it here so that the person who first adopted it (Toby?) or others can chip in.

    I hadn’t seen the notation \stackrel\circ\ni for a neighbourhood before, but it looks like a reasonable notation that I might want to adapt. BUT it seems more appropriate for a neighbourhood of a point rather than a neighbourhood of a set. Wouldn’t \stackrel\circ\supset or \stackrel\circ\supseteq be more appropriate for that case? What is the rationale for the usage on that page?

    • CommentRowNumber2.
    • CommentAuthorHarry Gindi
    • CommentTimeJun 22nd 2010

    Unicode has glyphs for open subset and open superset

    • CommentRowNumber3.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 22nd 2010

    What are they?

    Not sure they’d be right here because we don’t want to say “UU is an open subset of XX” but rather “UU is a neighbourhood of FF”. I’m guessing that the notation is meant to suggest “FF is a subset of the interior of UU”.

    • CommentRowNumber4.
    • CommentAuthorHarry Gindi
    • CommentTimeJun 22nd 2010
    • (edited Jun 22nd 2010)

    I can’t actually write them down (and I tried to make them in LaTeX, but I gave up). It’s a \circ in the middle of a \subset (don’t bother trying to make it in LaTeX, the symbols are aligned differently and can’t be composed without doing some serious work with hboxes and vboxes).

    • CommentRowNumber5.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 22nd 2010

    Ah, I see. You mean ⟃ (and ⟄). So one would write UXU ⟃ X for “UXU \subset X and UU open”.

    (To coin a phrase: iTeX rocks, dude)

    • CommentRowNumber6.
    • CommentAuthorHarry Gindi
    • CommentTimeJun 22nd 2010
    • (edited Jun 22nd 2010)

    Yeah. There’s also a symbol for “closed subset”.

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeJun 23rd 2010

    Yes, ‘\stackrel\circ\ni’ should be for a neighbourhood of a point, not for a neighbourhood of a set. (And as far as I know, it’s due to me.) For a neighbourhood of a set, ‘\stackrel\circ\supseteq’ would be good (and is due to Harald).

    • CommentRowNumber8.
    • CommentAuthorTobyBartels
    • CommentTimeJun 23rd 2010

    I’ve fixed the article.

    • CommentRowNumber9.
    • CommentAuthorHarry Gindi
    • CommentTimeJun 23rd 2010

    Hey, Toby, you realize that \ni means “such that”, right?

    • CommentRowNumber10.
    • CommentAuthorTobyBartels
    • CommentTimeJun 23rd 2010

    @ Harry:

    It can, but it also means ‘owns’; that is, AxA \ni x if and only if xAx \in A. Furthermore, there is a fuller form of the ‘such that’ symbol that allows you distinguish it from the ‘owns’ symbol. (Sorry I cannot find it in Unicode, but it amounts to continuing the horizontal line farther to the right.) Finally, there is no need for a symbol that stands for ‘such that’ in the first place! For example, there is no reason to write ‘xP(x)\exists x \ni P(x)’, you just write ‘xP(x)\exists x\, P(x)’. (Sometimes it’s nice to have some punctuation here, such as a comma, but that holds just as well with ‘\forall’.)

    • CommentRowNumber11.
    • CommentAuthorMike Shulman
    • CommentTimeJun 23rd 2010

    I detest the usage of \ni to mean “such that.” (Although I mean that in the nicest possible way, of course. (-: ) I think mathematics makes much more sense if writing a relation symbol backwards means reversing the variables in the relation, cf. x<yx\lt y and y>xy\gt x.

    I usually pronounce \ni as “contains,” although I guess that could also be used to mean \supseteq. Fortunately, in ETCS an element of a set is exactly the same as a singleton subset. (-:

    • CommentRowNumber12.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 23rd 2010

    Maybe I’m just making this up, but I thought I remembered Freyd calling it “ni”, as in the knights who say… ni!

    • CommentRowNumber13.
    • CommentAuthorGuest
    • CommentTimeJun 23rd 2010
    Well, ∋ is written \ni in TeX …

    - Harald H-O
    • CommentRowNumber14.
    • CommentAuthorHarry Gindi
    • CommentTimeJun 23rd 2010
    • (edited Jun 23rd 2010)

    I detest the usage of \ni to mean “such that.” (Although I mean that in the nicest possible way, of course. (-: ) I think mathematics makes much more sense if writing a relation symbol backwards means reversing the variables in the relation, cf. x<yx\lt y and y>xy\gt x.

    Blame Stephen DeBacker for getting my freshman class hooked on \ni.

    • CommentRowNumber15.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 23rd 2010

    I just remembered that and came back to admit my failure of memory, but you beat me to it, Harald! Actually, Freyd pronounces it “epsiloff”. :-)

    • CommentRowNumber16.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 24th 2010

    Back on track, I really like these notations for (essentially) “is in the interior of” or “the interior contains” for both an element or a subset. The link to the usual notation of the interior of a set makes it really easy to remember.

    Plus I can tell my topology students that this notation has been (partially) forged by someone in my own department! Who says mathematicians don’t do anything useful?

    Now all we need to do is get them into the unicode list. There’s ⫃ (and ⫄, ⋵, but no reverse of that one.) For the moment, I guess that the stackrel command produces a decent combination.

    Incidentally, Toby, did you mean ⋲ (and ⋺)? While I’m searching, here’s the closed subset notation (according to unicode): ⫏ ⫐ ⫑ ⫒

    There’s also standard entity ways of putting accents on top of letters; so a similar effect could be obtained by putting the appropriate accent on top of the subset symbol (this would be quite appropriate given Harald’s nationality!). So we could have ⊂ͦ and ⊃ͦ and ∊ͦ. Hmm, not quite centred on the “contained in” symbol there. Not sure how this would work in maths, though: F⊂ͦUF \mathop{&#x2282;&#x0366;} U versus FUF \stackrel\circ\subset U. No, the unicode version either gets separated or gets mangled a bit whatever I try.

    • CommentRowNumber17.
    • CommentAuthorTobyBartels
    • CommentTimeJun 24th 2010
    • (edited Jun 24th 2010)

    The accents aren’t really expected to work, since you’re putting an alphabetical accent on top of a mathematical symbol. They’ll look nice only if some coincidence in the fonts pertains. The Computer Modern fonts were, in part, designed to allow this sort of thing to work, but Unicode fonts generally aren’t.

    So <mover> (that’s math over) in MathML (which is what iTeX’s \stackrel and \overset produce) is probably the correct way to do it.

    Incidentally, Toby, did you mean ⋲ (and ⋺)?

    Thank you, Andrew, I meant ‘⋺’, but I couldn’t find it.

    By the way, am I the only one using a font on the Forum in which ‘⟃’ and its partner don’t look right? (‘⫑’ and its variants look fine.) Here is how it should look:

    ⟃

    I like these symbols too, although they serve a different purpose.

    • CommentRowNumber18.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 24th 2010

    By the way, am I the only one using a font on the Forum in which ‘⟃’ and its partner don’t look right?

    What font are you using? I’ve installed a firefox plugin that tells me exactly which font a particular glyph is being rendered in. For ⟃ (in text mode) it tells me that I’m using Trebuchet MS. It looks close enough to the picture that you drew - perhaps a little stretched horizontally, but not different enough to make me think that’s what you’re on about. It might be different in maths mode: &#x27C3;. Yes, there I get STIXGeneral. The Trebuchet one is a little lighter and so the circle seems further away from the enclosing symbol.

    • CommentRowNumber19.
    • CommentAuthorTobyBartels
    • CommentTimeJun 24th 2010

    I don’t think that I’m using any different fonts from whatever the Forum says to use. (Unless the Forum doesn’t say, in which case I seem to be using a default X sans-serif font, or DejaVu Serif in MathML.) On the Lab, I use DejaVu Sans outside MathML; that also doesn’t look right. The same bad look appears in MathML (DejaVu Serif) and fixed pitch (some default X monospace).

    Incidentally, the bad look in question is that the circle is the same height as the subset symbol, but centred farther to the left, so that it looks somewhat like what $O\!\!C$ would produce in TeX.

    What plugin is this that identifies fonts? (And is there a plugin that identifies Unicode code point? I would kill for that!)

    • CommentRowNumber20.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 24th 2010

    One such is FontFinder:

    https://addons.mozilla.org/en-US/firefox/addon/4415

    Searching for “font” in the firefox addons and then filtering to “Web Developer” gives a few others, one of which shows the font in the right-click context menu, and another which displays it in firebug.

    The forum does suggest fonts, but if you don’t have the top one then it might be displaying a different one.

    • CommentRowNumber21.
    • CommentAuthorTobyBartels
    • CommentTimeJun 24th 2010

    Thanks, Andrew!

    FontFinder says that the font on the problematic symbol is Trebuchet MS, or STIXGeneral in math mode.

    • CommentRowNumber22.
    • CommentAuthorAndrew Stacey
    • CommentTimeJun 24th 2010

    Strange, that’s what I was told too. Did it look wrong in both text and maths mode? Have you installed the recent release of the stix fonts?

    • CommentRowNumber23.
    • CommentAuthorTobyBartels
    • CommentTimeJun 24th 2010

    Did it look wrong in both text and maths mode?

    Yes.

    Have you installed the recent release of the stix fonts?

    No, unless my package manager suggested it to me automatically, in which case I did. But that wouldn’t explain the text-mode mismatch.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)