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Comment by orlp | Hacker News Reader

You're right I should've used "as a symbol" not "as the symbol". It's not terribly common.

Now that I think about it, most double stroked characters really represent "concrete" objects, not generic ones. Like ℙ for projective space, or 𝔸 for affine space. Also 𝔽 is often used together with an index 𝔽_q for the field with q elements.

On the other hand, Wikipedia[1] agrees with you, that 𝕏 is "occasionally" used for metric spaces.

[1] https://en.wikipedia.org/wiki/Blackboard_bold

My experience with 𝔽 is “vector space over a field 𝔽”, which is not a concrete object, but I have probably seen F written in a normal italic style more often.

As a counterpoint, 𝔽 when not fixed to a particular size is arguably still generic over "any field", and 𝔾 is most definitely generic for "any group", even if fixed to a particular size.

There might be small cultural differences at hand here. As a German, I prefer "k" or "K" for fields (as in "Körper"), and I think I've seen 𝔾 mostly as 𝔾_a or 𝔾_m for the additive and multiplicative group. shrug

I've seen ℙ used for probability.

I’ve also seen ⅆ as the differential operator and 𝔼(X) as the expected value of X. I think I’ve also seen 𝟙_x, and ⅈ, and ⅉ but I don’t remember for what.

I know 𝟙_X as the indicator function (also called characteristic function) of X in measure theory and probability theory, but I’ve also seen 1_X or χ_X.

ⅈ and ⅉ can be basis vectors or imaginary units although I’ve never seen them in blackboard bold in my lectures.

In set theory blackboard bold P, Q and C are very often used for arbitrary (forcing) posets

I've seen (and used) \mathbb{P} and \mathbb{E} for the probability & expectation operators (so not really a "concrete" object in your sense?)

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