query: Real number with lower limit topology is not 2nd countable
positive_passages.docid: 62793
positive_passages.text: $\mathbb{R}$ with the lower limit topology is not second-countable
negative_passages.docid: 34298
negative_passages.text: sequentially continuous on a non first-countable
negative_passages.docid: 17022
negative_passages.text: Definable real numbers
negative_passages.docid: 56646
negative_passages.text: Arithmetic progression topology
negative_passages.docid: 36248
negative_passages.text: A classical problem about limit of continuous function at infinity and its connection with Baire Category Theorem
negative_passages.docid: 2269
negative_passages.text: Proof that the real numbers are countable: Help with why this is wrong
negative_passages.docid: 75019
negative_passages.text: Infinite Cartesian product of countable sets is uncountable
negative_passages.docid: 148507
negative_passages.text: Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
negative_passages.docid: 19297
negative_passages.text: Is the cofinite topology on an uncountable set first countable?
negative_passages.docid: 136321
negative_passages.text: Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable.
negative_passages.docid: 70048
negative_passages.text: In which topologies do open sets maintain open under countable or arbitrary intersection?
negative_passages.docid: 11959
negative_passages.text: What's wrong with this argument that $[0,1]$ is countable?
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 83185
negative_passages.text: How to show countability of $\omega^\omega$ or $\epsilon_0$ in ZF?
negative_passages.docid: 70196
negative_passages.text: Is there any well-ordered uncountable set of real numbers under the original ordering?
negative_passages.docid: 324
negative_passages.text: Show uncountable set of real numbers has a point of accumulation
negative_passages.docid: 157513
negative_passages.text: How can I prove that these sets are countable infinite?