query: Proof that the continuous image of a compact set is compact
positive_passages.docid: 28637
positive_passages.text: Proving continuous image of compact sets are compact
negative_passages.docid: 78763
negative_passages.text: Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
negative_passages.docid: 32630
negative_passages.text: Proving that a set in which any sequence having exactly one accumulation point converges is compact
negative_passages.docid: 153573
negative_passages.text: Counter Example for the union of any number of compact sets is compact in T2-spaces
negative_passages.docid: 50366
negative_passages.text: Convolution is uniformly continuous and bounded
negative_passages.docid: 136583
negative_passages.text: Infimum is a continuous function, compact set
negative_passages.docid: 127173
negative_passages.text: Closed subset of compact set is compact
negative_passages.docid: 90152
negative_passages.text: Continuous with compact support implies uniform continuity
negative_passages.docid: 146146
negative_passages.text: Proof that a closed subset of a compact space is a compact space
negative_passages.docid: 30210
negative_passages.text: A compact operator is completely continuous.
negative_passages.docid: 138167
negative_passages.text: Image of a normal space under a closed and continuous map is normal
negative_passages.docid: 18040
negative_passages.text: Show that a compact metric space is bounded
negative_passages.docid: 98609
negative_passages.text: Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
negative_passages.docid: 64260
negative_passages.text: Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
negative_passages.docid: 74311
negative_passages.text: Proving that the Intersection of any Collection of Compact Sets is Compact
negative_passages.docid: 48783
negative_passages.text: Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
negative_passages.docid: 97761
negative_passages.text: Show that a proper continuous map from $X$ to locally compact $Y$ is closed