query: Prove that set of all limit points of a connected set is connected
positive_passages.docid: 144383
positive_passages.text: The closure of a connected set in a topological space is connected
negative_passages.docid: 2575
negative_passages.text: Showing that $\mathbb{R}$ is connected
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: 47820
negative_passages.text: How can I show a supremum of a set is also its limit point?
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: 102598
negative_passages.text: Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
negative_passages.docid: 108394
negative_passages.text: Proof of that every interval is connected
negative_passages.docid: 136158
negative_passages.text: $X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
negative_passages.docid: 116866
negative_passages.text: $A\times B$ connected component implies $A,B$ connect components
negative_passages.docid: 128482
negative_passages.text: The set of subsequential limits is closed
negative_passages.docid: 35069
negative_passages.text: Connectedness of the boundary
negative_passages.docid: 136851
negative_passages.text: Proof that the set of subsequential limits is closed
negative_passages.docid: 28641
negative_passages.text: Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected
negative_passages.docid: 104411
negative_passages.text: sum of two connected subset of $\mathbb{R}$
negative_passages.docid: 21820
negative_passages.text: How to prove that a set is invariant?
negative_passages.docid: 93623
negative_passages.text: Showing that every connected open set in a locally path connected space is path connected
negative_passages.docid: 48557
negative_passages.text: Product of connected spaces