Cardinality of continuous functions $f:\Bbb R\to \Bbb R$
12003
Cardinality of set of real continuous functions
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
128911
Continuous extension of a real function
2142
Finding a set of continuous functions with a certain property 2
41690
Products of Continuous functions: Topology
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
93330
Cardinality of all cardinalities
122086
continuous function: preimage of closure of a set is closure of preimage
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
146436
Cardinality of the set of bijective functions on $\mathbb{N}$?
70164
Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
54403
Given $f : \Bbb{R} \to \Bbb{R}$ is a continuous function. To prove that $\int_{0}^{1}f(x)x^2 dx = \frac{f(c)}{3}$ for some $c \in [0,1]$
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
68143
The set of convergent points of a sequence of continuous functions is Borel
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?