query: show that$ X$ is uncountable if $(X,d)$ is connected
positive_passages.docid: 84791
positive_passages.text: Is every connected metric space with at least two points uncountable?
negative_passages.docid: 55944
negative_passages.text: Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
negative_passages.docid: 112731
negative_passages.text: If $Y$ is connected, why is $A\cup Y$ connected in this case?
negative_passages.docid: 79568
negative_passages.text: Cardinality of the set $D$
negative_passages.docid: 67066
negative_passages.text: Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
negative_passages.docid: 108394
negative_passages.text: Proof of that every interval is connected
negative_passages.docid: 83842
negative_passages.text: Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
negative_passages.docid: 62911
negative_passages.text: Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
negative_passages.docid: 26919
negative_passages.text: Intersection of Connected Sets
negative_passages.docid: 84492
negative_passages.text: Can $X$ have compact connected components?
negative_passages.docid: 57943
negative_passages.text: If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
negative_passages.docid: 39455
negative_passages.text: Prove that $(X\times Y)\setminus (A\times B)$ is connected
negative_passages.docid: 156335
negative_passages.text: Proving Power Set of $\mathbb N$ is Uncountable
negative_passages.docid: 19599
negative_passages.text: $ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
negative_passages.docid: 108052
negative_passages.text: Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
negative_passages.docid: 18360
negative_passages.text: Proof that the irrational numbers are uncountable
negative_passages.docid: 84654
negative_passages.text: The graph of xy = 1 is connected or not