MathOverflow

I have a question about the following example from Algebraic spaces and quotients by equivalence relation of schemes by Roy Mikael Skjelnes (page 12)of a presheaf quotient, whichhas associated sheaf which can not be a scheme.It originally comes from...

It is known that a sequence of continuous functions on a metric space that converges pointwise on a dense subset need not converge pointwise on the full space. But what about if one assumes uniform continuity? Let me be more precise:
Let $X$ be a metric space and let $r_\alpha$ (for $\alpha=1,2,\ldots$) be a sequence of uniformly continuous functions $r_\alpha:X\to\mathbb{R}$. Furthermore, assume that $r:X\to\mathbb{R}$ is a uniformly continuous function such that $\lim_{\alpha\to...

Let $G$ be a locally compact abelian group and let $\widehat{G}$ denote its dual group, and let $L^{1}(G)$ and $L^{2}(G)$ be defined via the Haar measure.Consider the space$$K^{1}(G):=\{ h\in L^{1}(G) \; | \; \widehat{h}\in C_{c}(\widehat{G}) \} \; ...

Let $x \in \mathbb{R}^n$, let $k$ be a radial basis function (RBF) kernel
$$k(x, x') := \exp \left(-\frac{\|x-x'\|^2}{2\sigma^2}\right)$$
and let $\mathbf{K}$ be the following $n \times n$ covariance matrix