Give a bijection $f: (c,d) \to \Bbb R$ (f no trigonometric) to prove every open interval has the same cardinality of R
94363
Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
137883
Cardinality of the set of all (real) discontinuous functions
47903
How to prove every closed interval in R is compact?
93017
Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
13273
Cardinality of the set of all real functions of real variable
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
102972
Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
74502
Proving the bijection of a continuous function $f$ such that $|f(x)-f(y)| \geq \log(1+|x-y|) \forall x,y$ in $\mathbb{R}.$
22210
Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
47639
Uncountable Cartesian product of closed interval
27855
Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.