32 How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set? 27 Showing that the closure of a totally bounded set is totally bounded 23 What is the sum of all positive even divisors of 1000? 20 The closure of a connected set in a topological space is connected 19 Why aren't vacuous truths just undefined?

### Reputation (17,262)

 +10 Question on integral, notation and Nikodym derivative +10 How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set? +10 $A\cup B$ is connected when $A$ is connected in $X$ and $B$ clopen in $X-A$ -2 The closure of a connected set in a topological space is connected

### Questions (20)

 17 A general "inclusion-exclusion principle" / Formulas like $\inf(a,b)\sup(a,b)=ab$ 14 Prove that a covering map is a homeomorphism 13 Dual and completion of metric spaces 9 Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)? 9 Non-measurable set in product $\sigma$-algebra s.t. every section is measurable.

### Tags (253)

 281 real-analysis × 127 89 measure-theory × 54 223 general-topology × 63 87 analysis × 38 127 functional-analysis × 72 70 calculus × 35 93 abstract-algebra × 47 62 metric-spaces × 37 89 linear-algebra × 55 58 group-theory × 23

### Bookmarks (37)

 102 Why are vector spaces not isomorphic to their duals? 64 Does every set have a group structure? 58 Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ 51 What is the cardinality of the set of all topologies on $\mathbb{R}$? 45 Is there a topology $T$ on the set of complex numbers such that the class of $T$-continuous functions and the class of analytic functions coincide?

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