query: The graph of $f$ is a connected subset of $\mathbb{R}^2$.
positive_passages.docid: 27581
positive_passages.text: Topologist's sine curve is connected
negative_passages.docid: 7665
negative_passages.text: If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.
negative_passages.docid: 144383
negative_passages.text: The closure of a connected set in a topological space is connected
negative_passages.docid: 15487
negative_passages.text: Continuous function from a connected set?
negative_passages.docid: 156520
negative_passages.text: Intervals are connected and the only connected sets in $\mathbb{R}$
negative_passages.docid: 140929
negative_passages.text: Increasing, continuous function implies connectivity and viceversa.
negative_passages.docid: 30079
negative_passages.text: Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
negative_passages.docid: 39746
negative_passages.text: How to prove that given set is a connected subset of the space of matrices?
negative_passages.docid: 18039
negative_passages.text: Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
negative_passages.docid: 16517
negative_passages.text: Arcwise connected part of $\mathbb R^2$
negative_passages.docid: 116494
negative_passages.text: What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?
negative_passages.docid: 31266
negative_passages.text: Proof of "the continuous image of a connected set is connected"
negative_passages.docid: 153492
negative_passages.text: Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
negative_passages.docid: 39455
negative_passages.text: Prove that $(X\times Y)\setminus (A\times B)$ is connected
negative_passages.docid: 48692
negative_passages.text: A problem about the graph theory
negative_passages.docid: 135256
negative_passages.text: The fiber of a covering space over a connected space has constant cardinality
negative_passages.docid: 112731
negative_passages.text: If $Y$ is connected, why is $A\cup Y$ connected in this case?