Talk:Dual system

Changes as of 18th Feb 21

@Quondum: Especially, if $K\in \{\mathbb {R} ,\mathbb {C} \}$ we denote it by $\mathbb {K}$ or $\mathbb {k}$ or 𝕂, so that we notice that it is NOT a variable. –Nomen4Omen (talk) 19:17, 18 February 2021 (UTC)

Perhaps not the kind of variable as most people think of it, but here it is a variable that takes values that are sets (or fields). There are numerous articles in mathematics in WP that denote an unspecified field as K or F, for example the articles Field (mathematics), Finite field, Algebra over a field, Vector space, Matrix (mathematics) § Matrices with more general entries, Exterior algebra. —Quondum 20:14, 18 February 2021 (UTC)

Is black-board K a neologism of some kind? I can see why it is appealing, but I've never seen in any math book I've ever read, nor have I seen it in Wikipedia, up until today. 67.198.37.16 (talk) 05:09, 26 November 2023 (UTC)

Making the separation axioms "type check"

In (both) the separation axioms (copied below) we use equations like $b(x,\,\cdot )=0$. Here we are setting a function (or a functional) equal to 0, but it could be ambiguous if the 0 is the constant zero function (i.e., the zero functional) or the zero vector in the primal space. If it were interpreted as the zero vector in the primal space, then a reader might interpret this as $\exists x,\exists y,\,b(x,\,y)=0$, rather than $\exists x,\forall y,\,b(x,\,y)=0$, as intended.

A plain reading seems to imply that $\langle x,0\rangle =0\implies x=0$ when $\langle \cdot ,\cdot \rangle$ is a dual pairing.

Perhaps the alternative definition provided after the first is sufficient to ignore the ambiguity.

1. $Y$ separates (distinguishes) points of $X$: if $x\in X$ is such that $b(x,\,\cdot \,)=0$ then $x=0$; or equivalently, for all non-zero $x\in X$, the map $b(x,\,\cdot \,):Y\to \mathbb {K}$ is not identically $0$ (i.e. there exists a $y\in Y$ such that $b(x,y)\neq 0$ for each $x\in X$);

Tbardwell (talk) 15:32, 5 November 2025 (UTC)

Problem with math expressions in sections titles when shown on the contents sections

Sections titles with math on them, when shown on the contents, appear like

Identification of '"`UNIQ--postMath-0000009D-QINU`"' with '"`UNIQ--postMath-0000009E-QINU`"'

--~2026-71173-4 (talk) 00:26, 2 February 2026 (UTC)

An example you'll be able to see on this very talk page contents section $(X,Y)$

@Hadia maqbool ~2026-20708-56 (talk) 15:27, 4 April 2026 (UTC)