Let K = B [0, 1] be the ring of the continuous functions of [0, 1] in $ \mathbb{R}$ with the usual sum and...
104377
Maximal Ideals in Ring of Continuous Functions
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
72642
Continuous bijection from $(a,b) \to S^1$?
116883
About ideals in a ring which is a $k$ vector space
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
17139
Ring of holomorphic functions
54797
Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
117649
$f:[0,1]\to[0,1]$ be a continuous function. Let $x_1\in[0,1]$ and define $x_{n+1}={\sum_{i=1}^n f(x_i)\over n}$.Prove, $\{x_n\}$ is convergent
87617
Ring of $\mathbb{Z}_2$-valued functions
98772
Continuity of a function in $\mathbb{R}$
47419
Asymptotics of uniformly continuous functions over $\mathbb R$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
55243
When is the ring of continuous functions Noetherian?