query: If $\Bbb R$ has the half-open interval topology. Then is $\Bbb R \times \Bbb R$ not normal?
positive_passages.docid: 157287
positive_passages.text: Is there a simple method to prove that the square of the Sorgenfrey line is not normal?
negative_passages.docid: 116768
negative_passages.text: Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
negative_passages.docid: 66239
negative_passages.text: Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
negative_passages.docid: 28500
negative_passages.text: What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?
negative_passages.docid: 94363
negative_passages.text: Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
negative_passages.docid: 4156
negative_passages.text: What is $\Bbb R^{\times}$? [unit group, ring to "times" power]
negative_passages.docid: 11405
negative_passages.text: If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
negative_passages.docid: 86537
negative_passages.text: Prove that an open interval and a closed interval are not homeomorphic
negative_passages.docid: 70048
negative_passages.text: In which topologies do open sets maintain open under countable or arbitrary intersection?
negative_passages.docid: 62793
negative_passages.text: $\mathbb{R}$ with the lower limit topology is not second-countable
negative_passages.docid: 24351
negative_passages.text: The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
negative_passages.docid: 6491
negative_passages.text: Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
negative_passages.docid: 93017
negative_passages.text: Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
negative_passages.docid: 96363
negative_passages.text: How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
negative_passages.docid: 5250
negative_passages.text: Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?
negative_passages.docid: 59424
negative_passages.text: Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
negative_passages.docid: 44704
negative_passages.text: familly of Radially open sets in $\mathbb{R}^2$