Prove that if $ K_{A} $ is continuous then $FrA =\emptyset$
70617
Continuity at a point of characteristic function iff the point is not boundary point
58664
Proving a function is continuous for a fixed variable
157603
Continuity $\iff$ Preimage is closed whenever set is closed
40915
Proof if $f$ continuous in $x_0$ then there is a neighbourhood of $x_0$ so f bounded.
34836
Composition of Absolutely Continuous Functions
53627
Proving continuity of $f$
66758
$f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
87239
Prove functions defined by sup and inf are continuous
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.
23436
$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
79767
Properties of $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$ where $\{a_n\}$ is unbounded, strictly increasing sequence of positive reals
122086
continuous function: preimage of closure of a set is closure of preimage
84512
The preimage of continuous function on a closed set is closed.
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
135661
Weakly continuous operators are continuous
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$