query: Inclusions regarding the limsup and liminf of sets: $ \liminf E_n \subset \limsup E_n $
positive_passages.docid: 18907
positive_passages.text: Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
negative_passages.docid: 154578
negative_passages.text: Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
negative_passages.docid: 150995
negative_passages.text: Show that $\liminf(\sqrt{x_n})=\sqrt{\liminf x_n}$
negative_passages.docid: 47056
negative_passages.text: Show that the boundary of a set equals the boundary of its complement
negative_passages.docid: 146664
negative_passages.text: The union of two linearly independent subsets
negative_passages.docid: 66824
negative_passages.text: Two definitions of $\limsup$
negative_passages.docid: 56728
negative_passages.text: Question about limit points of a Subset of $\mathbb{R}$
negative_passages.docid: 11834
negative_passages.text: Prove that $\liminf x_n = -\limsup (-x_n)$
negative_passages.docid: 8414
negative_passages.text: Proof verification: Set of partial limits of a sequence is closed
negative_passages.docid: 1307
negative_passages.text: Infimum and supremum of the empty set
negative_passages.docid: 55614
negative_passages.text: Prove that a set consisting of a sequence and its limit point is closed
negative_passages.docid: 59162
negative_passages.text: Prove $\liminf\limits_{n\to\infty} F(x_n)\le F(x)$
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 80350
negative_passages.text: $\limsup \frac{a_n}{b_n}0$ s.t $a_n\le Mb_n$
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 157218
negative_passages.text: If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
negative_passages.docid: 136384
negative_passages.text: Inequality concerning limsup and liminf of Cesaro mean of a sequence