If $X$ is an order topology and $Y \subset X$ is closed, do the subspace topology and order topology on $Y$ coincide?

No. For example, let $X$ be $\mathbb{Q}$ with its standard ordering and let $Y$ be $([0,\sqrt{2}] \cap \mathbb{Q})\cup \{2\}$. Then $Y$ is closed in $X$ but the two topologies do not coincide: $2$ is isolated in the subspace topology but not in the order topology.

Classify finitely generated modules over the ring $\mathbb{C}[\epsilon]$ where $\epsilon^2=0$

When $L^p \subset L^q$ for $p <q$.

Angle between two planes in four dimensions

Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$

If $ax^2-bx+c=0$ has two distinct real roots lying in the interval $(0,1)$ $a,b,c$ belongs to natural prove that $\log_5 {abc}\geq2$

Does there exist a set of exactly five positive integers such that the sum of any three distinct elements is prime?

Coordinate ring of the unit circle is never a UFD?

Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.

Applications of additive version of Hilbert's theorem 90

Hardy's inequality again

Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain. [duplicate]

Proof $\int_0^\infty \frac{\exp(-\sqrt{x^2+y^2})}{x^2+y^2}dx = \frac{\pi}{2}\left(\frac{1}{y} - K_0(y)L_{-1}(y) - K_1(y)L_{0}(y)\right)$