Prove that the collection of arithmetic progressions $A=A_{a,b}|a,b\in \boldsymbol{Z},$b$\not\equiv 0$ is Basis for topology on $Z$
56646
Arithmetic progression topology
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
139078
Infinite partition of $\mathbb N$ by infinite subsets
101179
Partition of a set and Hall's theorem
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
57037
How does $(a,b)$ where $a,b\in \mathbb{Q}$ form a basis for $\mathbb{R}$?
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
72190
Topological proof on discrete topology where $X$ is infinite
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
136167
Prove that structure $(Q/{0}; =;*)$ has infinite number of automorphisms
151467
An infinite generating set of a finite dimensional vector space contains a basis
102112
Idempotents in $\mathbb Z_n$
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
62687
Proving Cardinality of Cosets in Abstract Algebra
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?
116768
Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology