Every bijection $f:\Bbb{R}\rightarrow[0,\infty)$ has infinitely many points of discontinuity.
22210
Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
32340
Continuous bijections and their inverses
12825
Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
14322
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
139078
Infinite partition of $\mathbb N$ by infinite subsets
155777
Show that infinite Cartesian product is uncountable
146436
Cardinality of the set of bijective functions on $\mathbb{N}$?
116494
What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
136167
Prove that structure $(Q/{0}; =;*)$ has infinite number of automorphisms
66301
The cardinality of the set of countably infinite subsets of an infinite set
109643
Prove that every isometry on $\mathbb{R}^2$ is bijective
94363
Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$