query: If X and Y are closed subsets of $\mathbb{R} $ , what if X is closed and Y is compact then is X+Y compact
positive_passages.docid: 28683
positive_passages.text: Sum of two closed sets in $\mathbb R$ is closed?
negative_passages.docid: 3708
negative_passages.text: How can I prove that compact subset iff sequentially compact in second countable topological spaces?
negative_passages.docid: 60424
negative_passages.text: Uncountable family of uncountable compact subsets of $\mathbb{R}$
negative_passages.docid: 81927
negative_passages.text: Example of closed and bounded in $\mathbb Q$ set that is not compact
negative_passages.docid: 47903
negative_passages.text: How to prove every closed interval in R is compact?
negative_passages.docid: 29303
negative_passages.text: Cartesian product of compact sets is compact
negative_passages.docid: 65358
negative_passages.text: Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
negative_passages.docid: 22131
negative_passages.text: Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
negative_passages.docid: 31559
negative_passages.text: If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
negative_passages.docid: 106957
negative_passages.text: Compact sets are closed?
negative_passages.docid: 48783
negative_passages.text: Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 147914
negative_passages.text: Closed image of locally compact space
negative_passages.docid: 64694
negative_passages.text: $C_{c}(X)$ is complete. then implies that $X$ is compact.
negative_passages.docid: 136108
negative_passages.text: Arbitrary intersection of closed, connected subsets of a compact space connected?
negative_passages.docid: 116663
negative_passages.text: If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
negative_passages.docid: 11405
negative_passages.text: If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?