Is $\Bbb{Z}$ compact under the evenly spaced integer topology?

The collection $$p\mathbb{Z}$$ as $p$ ranges over primes covers all but one and minus one. If I then include $$ 5\mathbb{Z}+1$$ and $$5\mathbb{Z}-1$$ has that a finite subcover?

Tags:

General Topology

Compactness

Ideals

Integers

Related

Can every positive real number $\leqslant\frac{\pi^2}6$ be expressed in this form? Show that $\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt{n}}\sin(1 + \frac{x}{n})$ converges uniformly on $\mathbb{R}$ Everyone loves all lovers, Romeo loves Juliet $\vdash$ I love you (Natural deduction proof) If $\lim_{x\to 0}{f(x)} = \lim_{x\to 0}{g(x)}=0$, then is $\lim_{x\to 0}\frac{\sin f(x)}{g(x)}= \lim_{x\to 0}\frac {f(x)} {g(x)}$? Limit of the ratio of two non-Riemann sums. Reasoning behind the trigonometric substitution for $\sqrt{\frac{x-\alpha}{\beta-x}}$ and $\sqrt{(x-\alpha)(\beta-x)}$ End(M) for cyclic R-module M is a commutative ring where R is a PID. Find all integers $m,\ n$ such that $m^2+4n$ and $n^2+4m$ are both squares. functional equation $f(x^2)=xf(x)$ Can every manifold be turned into a Lie group? Why $r^{2} $ instead of $r^3$ in this change of variable? Can I search for factors of $\ (11!)!+11!+1\ $ efficiently?

Recent Posts