query: Is a function that maps every connected set to a connected set continuous?
positive_passages.docid: 77621
positive_passages.text: Continuity of function mapping connected set to connected set
negative_passages.docid: 99179
negative_passages.text: Continuous function with compact domain has continuous inverse
negative_passages.docid: 52388
negative_passages.text: The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
negative_passages.docid: 55238
negative_passages.text: Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
negative_passages.docid: 127739
negative_passages.text: Is a continuous function on a bounded set bounded itself?
negative_passages.docid: 23965
negative_passages.text: Function which preserves closed-boundedness and path-connectedness continuous?
negative_passages.docid: 91682
negative_passages.text: Graph of a continuous function is closed
negative_passages.docid: 83163
negative_passages.text: If $X$ is a connected metric space, then a locally constant function $f: X \to $ M, $M $ a metric space, is constant
negative_passages.docid: 72044
negative_passages.text: prove $x \mapsto x^2$ is continuous
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 152493
negative_passages.text: Is an expanding map on a compact metric space continuous?
negative_passages.docid: 143951
negative_passages.text: Can we determine uniform continuity from graphs?
negative_passages.docid: 40208
negative_passages.text: Locally Constant Functions on Connected Spaces are Constant
negative_passages.docid: 118048
negative_passages.text: Can a function with just one point in its domain be continuous?
negative_passages.docid: 68165
negative_passages.text: Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
negative_passages.docid: 26919
negative_passages.text: Intersection of Connected 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?