Can the set of all functions from $\mathbb{R}$ to $\mathbb{R}$ be defined?
75674
collection of all functions is a proper class
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
13273
Cardinality of the set of all real functions of real variable
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
152613
Injection from $\mathbb{N}\to\{0,1\}$ to the set of all monotonic decreasing functions from $\mathbb{N}\to\mathbb{Z}$
73850
Cardinality of set of functions
104842
Let $X$ be uncountable. Then the set of injective functions $f\colon X \to \mathbb{R}$ has empty interior in $\mathscr{C}(X;\mathbb{R})$
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
137883
Cardinality of the set of all (real) discontinuous functions
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
118154
$f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ twice
146055
Proving a set of functions is uncountable
105445
Are the rationals a closed or open set in $\mathbb{R}$?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$