Let $R$ be the ring of all continuous functions from the closed interval $[0,1]$ to $\mathbb {R}.$
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
125610
Space of bounded continuous functions is complete
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
122086
continuous function: preimage of closure of a set is closure of preimage
60700
Continuity of a function to the integers
129324
Let $f:[0;1]\to\mathbb R$ be continiously differentiable
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
24914
Does every continuous map from $\mathbb{Q}$ to $\mathbb{Q}$ extends continuously as a map from $\mathbb{R}$ to $\mathbb{R}$?
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
98772
Continuity of a function in $\mathbb{R}$
129371
Maximal ideals in the ring of real functions on $[0,1]$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$