query: Continuity in product, uniform, and box topologies
positive_passages.docid: 158221
positive_passages.text: Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
negative_passages.docid: 29303
negative_passages.text: Cartesian product of compact sets is compact
negative_passages.docid: 12490
negative_passages.text: A map is continuous if and only if for every set, the image of closure is contained in the closure of image
negative_passages.docid: 64619
negative_passages.text: Continuity of a function of product spaces
negative_passages.docid: 2198
negative_passages.text: Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
negative_passages.docid: 36150
negative_passages.text: Ideal in a ring of continuous functions
negative_passages.docid: 19566
negative_passages.text: Continuous images of compact sets are compact
negative_passages.docid: 154259
negative_passages.text: Countinuity of the identity map between different topologies
negative_passages.docid: 140168
negative_passages.text: What are the basis for co-countable and co-finite topologies
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 24050
negative_passages.text: Characterization of the Closure of a Set
negative_passages.docid: 138815
negative_passages.text: For which conditions on countable sets does continuity implies uniform continuity
negative_passages.docid: 15487
negative_passages.text: Continuous function from a connected set?
negative_passages.docid: 56440
negative_passages.text: Cartesian products and families
negative_passages.docid: 36227
negative_passages.text: Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
negative_passages.docid: 71916
negative_passages.text: Quasi-components and components coincide for compact Hausdorff spaces
negative_passages.docid: 143951
negative_passages.text: Can we determine uniform continuity from graphs?