query: compact subsets of $ \mathbb{R^2}$
positive_passages.docid: 22464
positive_passages.text: Which of the following subsets of   $\mathbb{R}^2$ are compact
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 69497
negative_passages.text: Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
negative_passages.docid: 116542
negative_passages.text: Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
negative_passages.docid: 127173
negative_passages.text: Closed subset of compact set is compact
negative_passages.docid: 41408
negative_passages.text: Which of the following sets are compact:
negative_passages.docid: 158498
negative_passages.text: $A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
negative_passages.docid: 156479
negative_passages.text: Fractal dimension of set in $\mathbb{R}^2$
negative_passages.docid: 95294
negative_passages.text: Dense subset of $C[0,1]$ which preserves rationals
negative_passages.docid: 70164
negative_passages.text: Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
negative_passages.docid: 2198
negative_passages.text: Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
negative_passages.docid: 11383
negative_passages.text: Disjoint compact sets in a Hausdorff space can be separated
negative_passages.docid: 146455
negative_passages.text: Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
negative_passages.docid: 128894
negative_passages.text: About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
negative_passages.docid: 95747
negative_passages.text: Number of countable subsets of $\mathbb{R}$
negative_passages.docid: 28637
negative_passages.text: Proving continuous image of compact sets are compact
negative_passages.docid: 143105
negative_passages.text: Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$