query: $(0,1)$ is an open subset of $\Bbb R$ but not of $\Bbb R^2$ when we think of $\Bbb R$ as the $x$-axis in $\Bbb R^2$.
positive_passages.docid: 21599
positive_passages.text: $(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 44430
negative_passages.text: Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
negative_passages.docid: 44522
negative_passages.text: Subsets of the reals when the Continuum Hypothesis is assumed false
negative_passages.docid: 147534
negative_passages.text: The set of irrational numbers is not a $F_{\sigma}$ set.
negative_passages.docid: 18334
negative_passages.text: Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
negative_passages.docid: 136106
negative_passages.text: Is every open subset of $ \mathbb{R} $ uncountable?
negative_passages.docid: 69542
negative_passages.text: Why do the $n \times n$ non-singular matrices form an "open" set?
negative_passages.docid: 2198
negative_passages.text: Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
negative_passages.docid: 60485
negative_passages.text: Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
negative_passages.docid: 153934
negative_passages.text: How to prove that a set R\Z is open
negative_passages.docid: 149317
negative_passages.text: An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
negative_passages.docid: 22464
negative_passages.text: Which of the following subsets of   $\mathbb{R}^2$ are compact
negative_passages.docid: 41872
negative_passages.text: Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
negative_passages.docid: 133808
negative_passages.text: A doubt from Milnor's "Topology from a Differentiable Viewpoint".
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set
negative_passages.docid: 36921
negative_passages.text: An Open Interval and a Half-open Interval are not Homeomorphic