query: Continuous function and induced homomorphism
positive_passages.docid: 149029
positive_passages.text: 3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 36149
negative_passages.text: A uniformly continuous function maps bounded set to bounded sets
negative_passages.docid: 130975
negative_passages.text: Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
negative_passages.docid: 52388
negative_passages.text: The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
negative_passages.docid: 120947
negative_passages.text: continuous real-valued function
negative_passages.docid: 19566
negative_passages.text: Continuous images of compact sets are compact
negative_passages.docid: 61122
negative_passages.text: A continuous mapping is determined by its values on a dense set
negative_passages.docid: 34836
negative_passages.text: Composition of Absolutely Continuous Functions
negative_passages.docid: 134703
negative_passages.text: Let $X$ be a connected space, $f:X\to X$ continuous involution, $g:X\to\mathbb{R}$ continuous. Prove that $\exists$ $x\in X$ such that $g(x)=g(f(x))$.
negative_passages.docid: 31266
negative_passages.text: Proof of "the continuous image of a connected set is connected"
negative_passages.docid: 57283
negative_passages.text: Extending Homomorphism into Algebraically Closed Field
negative_passages.docid: 29582
negative_passages.text: Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
negative_passages.docid: 121957
negative_passages.text: Is $p\mapsto \|f\|_p$ continuous?
negative_passages.docid: 135863
negative_passages.text: Is the graph of a continuous function homeomorphic to its domain?
negative_passages.docid: 65346
negative_passages.text: Characterisation of uniformly continuous function
negative_passages.docid: 61334
negative_passages.text: Application of Main Homomorphism Theorem