4 msยท
๐ is used as a symbol for a generic metric space. E.g. if your result is generic over โยฒ, โยณ, etc, you can write ๐.
by orlp 3y ago
๐ is used as a symbol for a generic metric space. E.g. if your result is generic over โยฒ, โยณ, etc, you can write ๐.
- dietrichepp 3y agoThanks! I am always a little curious about how these symbols are used. That makes perfect sense to me.
- red_trumpet 3y agoI'm a PhD student in algebraic geometry and have seldom seen this. IME "X" is a generic name for all kinds of spaces (metric, topological, complex analytic, algebraic...), but I don't remember ever having seen "๐". That said, in principal everyone is free to call their spaces how they like. It just makes it easier to read if one sticks to familiar notation.
- orlp 3y agoYou're right I should've used "as a symbol" not "as the symbol". It's not terribly common.
- red_trumpet 3y agoNow that I think about it, most double stroked characters really represent "concrete" objects, not generic ones. Like โ for projective space, or ๐ธ for affine space. Also ๐ฝ is often used together with an index ๐ฝ_q for the field with q elements. On the other hand, Wikipedia[1] agrees with you, that ๐ is "occasionally" used for metric spaces. [1] https://en.wikipedia.org/wiki/Blackboard_bold https://en.wikipedia.org/wiki/Blackboard_bold
- dietrichepp 3y agoMy experience with ๐ฝ is โvector space over a field ๐ฝโ, which is not a concrete object, but I have probably seen F written in a normal italic style more often.
- orlp 3y agoAs a counterpoint, ๐ฝ when not fixed to a particular size is arguably still generic over "any field", and ๐พ is most definitely generic for "any group", even if fixed to a particular size.
- red_trumpet 3y agoThere might be small cultural differences at hand here. As a German, I prefer "k" or "K" for fields (as in "Kรถrper"), and I think I've seen ๐พ mostly as ๐พ_a or ๐พ_m for the additive and multiplicative group. shrug
- dataflow 3y agoI've seen โ used for probability.
- runarberg 3y agoIโve also seen โ as the differential operator and ๐ผ(X) as the expected value of X. I think Iโve also seen ๐_x, and โ , and โ but I donโt remember for what.
- brewmarche 3y agoI know ๐_X as the indicator function (also called characteristic function) of X in measure theory and probability theory, but Iโve also seen 1_X or ฯ_X. โ and โ can be basis vectors or imaginary units although Iโve never seen them in blackboard bold in my lectures.
- ginnungagap 3y agoIn set theory blackboard bold P, Q and C are very often used for arbitrary (forcing) posets
- nephanth 3y agoI've seen (and used) \mathbb{P} and \mathbb{E} for the probability & expectation operators (so not really a "concrete" object in your sense?)