the $\sigma$ algeba generated by the class of open intervals with rational end points coincide with the borel $\sigma$ algebra on the real line.
10247
What is the minimum $ \sigma$-algebra that contains open intervals with rational endpoints
61810
An application of Borel-Caratheodory theorem
80945
Borel subalgebras contain solvable radical
106178
Question of an isomorphism of $\epsilon_ 0$ and a subset of the rationals.
133884
A proof using Yoneda lemma
44575
The sigma function (sum of divisors) multiplicative proof
42362
Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals
150385
The use of the Axiom of Choice in this proof of the sequence lemma
104308
Proving a set is a Sigma Algebra
55717
cardinality of the Borel $\sigma$-algebra of a second countable space
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
11082
Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick
47159
Wanted: example of an increasing sequence of $\sigma$-fields whose union is not a $\sigma$-field
23414
Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
87203
Preimage of generated $\sigma$-algebra