query: Prove that $\omega^{1}$ is closed.
positive_passages.docid: 20539
positive_passages.text: Differential form is closed if the integral over a curve is rational number.
negative_passages.docid: 36237
negative_passages.text: Closed set mapped to itself in a compact Hausdorff space
negative_passages.docid: 78399
negative_passages.text: In $T_1$ space, all singleton sets are closed?
negative_passages.docid: 138729
negative_passages.text: What happens when $\lvert\omega\rvert =1$?
negative_passages.docid: 13620
negative_passages.text: $\omega_2$ is a not countable union of countable sets without AC
negative_passages.docid: 112008
negative_passages.text: Ordinal $\omega_1$ is not compact
negative_passages.docid: 33310
negative_passages.text: Proving that the set of limit points of a set is closed
negative_passages.docid: 38221
negative_passages.text: What is wrong with this proof there is no $\omega$-th worldly cardinal
negative_passages.docid: 108642
negative_passages.text: $e^A$, where $A= \begin{bmatrix} 0 & \omega \\ -\omega& 0 \end{bmatrix}$
negative_passages.docid: 6270
negative_passages.text: Poincaré inequality for a subspace of $H^1(\Omega)$
negative_passages.docid: 158569
negative_passages.text: Proving a particular subset of $R^n$ is closed
negative_passages.docid: 41298
negative_passages.text: Understanding proof of completeness of $L^{\infty}$
negative_passages.docid: 110744
negative_passages.text: How to prove that a compact set in a Hausdorff topological space is closed?
negative_passages.docid: 152976
negative_passages.text: Real Analysis: open and closed sets
negative_passages.docid: 100608
negative_passages.text: Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
negative_passages.docid: 117508
negative_passages.text: Prove that the closed unit ball of $L^2[a,b]$ is closed in $L^1[a,b]$
negative_passages.docid: 55614
negative_passages.text: Prove that a set consisting of a sequence and its limit point is closed