Why $\{\omega :[0,1]\to \mathbb R\text{ continuous}\}$. is not in $\sigma \{(\omega :[0,1]\to \mathbb R\mid \omega (t_i)\in B_i\}$.?
105333
Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions
40576
Intermediate value property problem and continuous function
98772
Continuity of a function in $\mathbb{R}$
146306
A continuous surjective function from $(0,1]$ onto $[0,1]$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
25498
Prove that $\omega + \omega_1 = \omega \cdot \omega_1 = \omega^{\omega_1} = \omega_1$
10747
Given function $g$ continuous in line $[0,\infty)$...
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
38221
What is wrong with this proof there is no $\omega$-th worldly cardinal
139151
How to prove $\left\{ \omega|X(\omega)=Y(\omega)\right\} \in\mathcal{F}$ is measurable, if $X$ and $Y$ are measurable?
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
84092
If $id:(X,d_1)\to (X,d_2)$ is continuous then what will be $X$?