What does “finite rank” mean in the context of divisible abelian $q$-group? A divisible abelian $q$-group of finite rank is always a Prüfer $q$-group or it can be also a finite product of Prüfer $q$-group? Thanks for all future answers to my questions.

Definitions According to my linear programming course and screenshot here (Finnish), a polyhedron is such that it can be constrained by a finite amount of inequalities such that $$P=\{\bar x\in \mathbb R^n | A \bar x\geq \bar b\}, A\in \mathbb R^{m\times n},\bar b\in \mathbb R^m$$ and a convex function $f(x)$ must satisfy $$f(\lambda \bar x+(1-\lambda)\bar […]

Typical Terminology: A basis $\mathcal{B}$ for a topology on a set $X$ is a set of subsets of $X$ such that (i) for all $x\in X$ there is some $U\in\mathcal{B}$ such that $x\in U$, and (ii) if $x\in U\cap V$ for some $U,V\in\mathcal{B}$, then there is some $W\in\mathcal{B}$ such that $x\in W\subseteq U\cap V$. The […]

What are the equilibrium solutions for the differential equation $\dfrac{\mathrm{d}y}{\mathrm{d}t} = 0.2\left(y-3\right)\left(y+2\right)$ My Question: What does equilibrium solution mean in this context of this problem?

Functional analysis is ‘a kind of mathematical analysis’ where the object of study are functions. The tool for studying functions are the operators. A specific type of operators are the functionals. My question is why do we call this subject as functional analysis, while the main role here is the operator? And if someone has […]

I was recently reading about circle rotations (a basic example in dynamical systems) and got confused by some notation. It said consider the unit circle $S^{1} = [0,1]/{\sim}$, where $\sim$ indicates that $0$ and $1$ are identified. What does “identify” mean? and how is the set $[0,1]/{\sim}$ different from the set $[0,1]$? Thanks!

Not sure if this question is on topic. I am looking for a nice correct and succinct way to describe “2 lines are limiting parallel ” that is: Understandable for newbies to hyperbolic geometry. Geometrically correct not mentions “ideal points”. (because they don’t really exist. “going in the same direction” is also not allowable, lines […]

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions $f(x,y)$ (that have coordinates $x,y,z$) be called a 2D function if its plot is 3D? This is confusing and potentially ambiguous. […]

Is there a name for a topological space $X$ which satisfies the following condition: Every closed set in $X$ is contained in a countable union of compact sets Does Baire space satisfy this condition? Thank you!

If there are two “nice” shapes in $R^2$, such as circles or polygons, whose intersection has area 0, then they must be interior-disjoint, as their intersection can only contain pieces of their boundary. My question is: what is a simple term for those “nice” subsets of $R^2$ for which intersection of area 0 implies interior-disjointness? […]

Intereting Posts

Squaring across an inequality with an unknown number
Wanted: example of an increasing sequence of $\sigma$-fields whose union is not a $\sigma$-field
How does one evaluate $\sqrt{x + iy} + \sqrt{x – iy}$?
Prove that $\frac{\int_0^1xf^2(x) \mathrm{d}x}{\int_0^1 xf(x) \mathrm{d}x}\le\frac{\int_0^1 f^2(x) \mathrm{d}x}{\int_0^1 f(x) \mathrm{d}x}$
How to prove $f(\bigcap_{\alpha \in A}U_{\alpha}) \subseteq \bigcap_{\alpha \in A}f(U_{\alpha})$?
Sin(x): surjective and non-surjective with different codomain?
a theorem of Fermat
What dimensions are possible for contours of smooth non-constant $\mathbb R^n\to\mathbb R$ functions?
Proof for formula $\int e^{g(x)} dx = f(x) e^{g(x)}+C$
Suppose $F$ is a finite field of characteristic $p$. Prove $\exists u \in F$ such that $F = \mathbb{F}_{p}(u)$.
The cone of a topological space is contractible and simply connected
Is the number of primes congruent to 1 mod 6 equal to the number of primes congruent to 5 mod 6?
Sum of the squares of the reciprocals of the fixed points of the tangent function
The use of conjugacy class and centralizer?
Knot with genus $1$ and trivial Alexander polynomial?