For $A \subset X$ prove that $ f(\overline{A}) \subset \overline{f(A)}$
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
44912
Prove that $ \overline {A^\complement} = (A°)^\complement $
80009
Prove that $| |a|-|b| | \le |a-b|$
28391
Prove the compactness of a set B
40604
Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
98634
What is a counterexample for If $x\in\overline{A},$ $x$ is not necessarily a limit of a sequence in $A$?
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
154363
Prove that $\text{aff}(X) = \text{aff}(\text{closure}(X))$
40524
Let $A \subseteq (0,\infty$) such that $\inf A>0$. Let $\frac{1}{A}=\{\frac{1}{a},a\in A\}$. Prove that $\sup \frac{1}{A}=\frac{1}{\inf A}$.
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .