# All Questions

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### Is there any relation between a group being unimodular and having equivalent uniform structures?

Recall: A topological group is said to have equivalent uniform structures if its left and right uniform structures coincide. A locally compact group is said to be unimodular if left Haar measures and ...
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### Solving an integral when using a dummy variable

I'm trying to solve an integral and I don't remember how to when a variable is in the integral symbol, if that makes sense. I'm not sure what the correct terminology is. So day I have an integral ...
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### Proving that the genus of a nonsingular plane curve is $\frac{(d-1)(d-2)}{2}$

I'm studying from Joseph Silverman's book The Arithmetic Of Elliptic Curves and I'm trying to do as many exercises as I can. Right now I'm trying to do Exercise 2.7 from chapter II which reads as ...
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### Excision via simplicial sets

Let $X$ be a topological space, covered by a collection of open sets $\{U_\alpha\}$ (or more generally a cover by subspaces whose interiors cover $X$). Consider the singular simplicial set ...
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### About Cardinality in Hausdorff Spaces

I have two problems: 1.- Let $X$ be a compact Hausdorff space, then $X$ has a basis with cardinality less than or equal to $|X|$. 2.- Let $X$ be a Hausdorff space and $D$ a dense subset in $X$, ...
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### Why is $\infty^0$ indeterminate?

In a recent test question I was required to us L'Hopital's rule to evaluate: $$\lim_{x\to 0^+} x\ln{(e^{2x}-1)}$$ I assumed that anything multiplied by 0 would give an answer of 0. This turns out ...
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### Touch up on Trig

I have forgotten a few things about trigonometry and angles. I have this trig equation, $\sin \theta = \frac{200\text{ dyn}}{224\text{ dyn}}$ What exactly are the steps of getting the angle, ...
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Here is a question that has been posted on another forum (in french) that I couldn't answer and about which I'm really curious. So here it is, let's be given as a state space $\Omega=\{f\in ... 0answers 55 views ### Prove that single machine can reduce from 2-partition problem I'm given the following problem: Prove that single machine \sum U_i (number of tardy job) with release date constraints problem can reduce from 2-partition problem ... 1answer 64 views ### “full coverage” in hyperspherical space I'm working on a computer algorithm that considers the relationships between data points in a theoretical n-dimensional space. I am "looking" from the origin in all directions in a programmatic way ... 0answers 45 views ### How to construct certain cover given in Mumford's Abelian Varities book In chapter I, appendix to section 2 of the book "abelian varieties" by Mumford, we consider a discrete group$G$acting freely and discontinuously on a good topological space$X$(i.e.,$\forall x \in ...
I have function that is defined as $$Y = \frac{1}{15} x \longrightarrow {\rm if}\qquad 0 \leq x \leq 30$$ $$Y = \frac{1}{70} x + \frac{11}{7} \longrightarrow {\rm if}\qquad x > 30$$ The ...