Asking for clarification on the proof for Rudin's theorem 2.41: Equivalent properties of $E \subset \mathbb{R}^k$
109200
Baby Rudin theorem 2.41
44259
Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
140570
Suppose $E\subseteq\mathbb{R}$ is closed and $K\subseteq\mathbb{R}$ is compact. Show that every open cover of $E\cap K$ has a finite subcover
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
102485
Showing that a topological space is ${\rm T}_1$
9854
If $U$ is a neighborhood of $e$, there exists $V$ neighborhood of $e$ such that $V^{-1}V \subseteq U$
110635
Proving $\mathbb{N}^k$ is countable
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
35305
Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
37924
Equivalence of norms proof
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
106178
Question of an isomorphism of $\epsilon_ 0$ and a subset of the rationals.
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?