# Questions tagged [definitions]

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### In mathematics, what are some complicated objects that can be intuitively described using plain English? [closed]

I was thinking of the following problem: Let $X$ be a random variable that realizes a piece of observable (data) $x_n \in \mathbb{R}^n$ (say, vectorized images of cats), what is the meaning of the ...
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### What is a finitely connected domain?

(Cross-posted from MSE.) The paper Chang, S.-Y. A. and Yang, P. C.: Conformal deformation of metrics on S 2 . J. Differential Geom., 27(2), 1988 (DOI, MathSciNet) states in Proposition 2.3 that Moser'...
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### Two definitions of automorphic forms on Lie groups

My question is the about the equivalence of two definitions of automorphic forms on a semisimple Lie group. The most common definition of automorphic forms on a semisimple Lie group $G$ with respect ...
443 views

### Why are isotropic random vectors called isotropic if they aren't? [closed]

A random vector $X \in \mathbb{R}^n$ is isotropic if $\mathbb{E}XX^T = I_n$. However isotropic random vectors don't have the property of isotropy. See 1. So why are they called isotropic? Similarly a ...
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1 vote
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### What is the definition of Plancherel density?

I know about the Plancherel measure, but I don't know where the term "Plancherel density" is defined.
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### Terminology: "sufficiently large absolute constant"

I'm currently reading the paper "Random matrices: The distribution of the smallest singular values" by '"Terence Tao and Van Vu" and have run into some terminology which I don't quite (rigorously) ...
1 vote
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### Open/closed/constructible subsets of locally free sheaves

(Cross-posted from math.SE since I'm not sure what is a suitable platform. Link on https://math.stackexchange.com/questions/3597258/open-closed-constructible-subsets-of-locally-free-sheaves) Is there ...
Let $X,Y$ be topological spaces. The compact-open topology on $C(X,Y)$ is generated by the sub-basic open sets  \left\{U_{K,O}: \mbox{ K is compact in X and O is open in Y}\right\}\\ U_{K,O}:=\...