Proving there is a bijection from set of real continuous function on $[0,1]$ denoted by $C[0,1]$ to the set of reals $\mathbb{R}$
12003
Cardinality of set of real continuous functions
70264
Prove that the inverse image of an open set is open
324
Show uncountable set of real numbers has a point of accumulation
31266
Proof of "the continuous image of a connected set is connected"
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
117502
Proving that a certain continuous function is surjective.
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
131992
A problem on continuous functions
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
28637
Proving continuous image of compact sets are compact
141114
Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
143800
continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
2575
Showing that $\mathbb{R}$ is connected
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$