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 Jul 26 comment The Star Trek Problem in Williams's Book Why not try the problem in the one-dimensional setting and see what happens? Jul 19 awarded Critic Jul 4 comment History of Dual Spaces and Linear Functionals @MattE I like that explanation. In fact, that is exactly how it was done historically according to the stuff I have read. Jul 4 comment Dimension of a cyclic submodule of a finite group representation Isn't it true that the span of $\{\rho_g v : g \in G, v \in V\}$ is equal to the span of $\{\rho_g v : g \in G, v \in B\}$ where $B$ is any basis of $V$? If $G$ is finite, then you can compute the dimension of this latter span by checking for linear independence of the vectors in $\{\rho_g v : g \in G, v \in B\}$. Jul 4 comment Bound on $E[X Y]$, where $Y$ is bounded in terms of $X$ If $X \ge Y^k$, then $XY \ge Y^{k+1}$ and so $E[XY] \ge E[Y^{k+1}]$. I don't know what to do with $E[Y^{k+1}]$ though. Jul 3 comment History of Dual Spaces and Linear Functionals Nice. I will definitely have to read that book. Jul 3 answered History of Dual Spaces and Linear Functionals Jul 2 comment History of Dual Spaces and Linear Functionals I disagree that the concept of a linear functional occurs "everywhere". The two examples you gave are well and good but they will not force me to start thinking about linear functionals in general. I am wondering what Riesz's motivation was in producing the RRT. You mention that the RRT can be used to define the cross product using determinants. I find that interesting. Do you have a reference? Jul 2 comment History of Dual Spaces and Linear Functionals If I were exploring the difference between row vectors and column vectors, I would make two observations: row vector x column vector = scalar and column vector x row vector = matrix. That this would lead me to the concepts of linear functional or dual space seems unlikely to me. Jul 1 asked History of Dual Spaces and Linear Functionals Jun 13 comment Union of compact sets in a convergence space Ah, of course! Thanks a lot. Jun 13 accepted Union of compact sets in a convergence space Jun 13 comment Union of compact sets in a convergence space This is true if the convergence spaces are topological by the argument you just gave. The general case though... Jun 13 asked Union of compact sets in a convergence space Jun 8 awarded Caucus Jun 1 comment Continuous and Open maps A continuous function that maps open sets to open sets is just called an open map as far as I know. Apr 20 comment Is there a way of defining the notion of a variable mathematically? Thanks for the example. However, I am not convinced this clarifies what a variable is. Calling the symbol $x$ a variable when defining a polynomial ring $F[x]$ does not define what a variable is. Apr 20 accepted Is there a way of defining the notion of a variable mathematically? Apr 19 comment The topology of distributions Excellent. Thanks. Apr 19 comment Is there a way of defining the notion of a variable mathematically? I do not see the connection. Can you give me a concrete example?