A linear form $f$ is continuous respect to weak$^{\star}$ topology if and only if there exists $x \in E$ such that $f(x')=x'(x)$ for all $x'\in E'$.
118323
What is the topological dual of a dual space with the weak* topology?
42913
Equivalence of the definition of the Subbasis of a Topology
126881
(weak) homotopy equivalence
41690
Products of Continuous functions: Topology
31266
Proof of "the continuous image of a connected set is connected"
128911
Continuous extension of a real function
117897
A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
133422
How to prove the continuity of an induced map; $g_* : C(X, Y) \rightarrow C(X, R)$, induced from the map $g \in C(Y, R)$, endowed with fine topology.
83046
A linear map, continuous at zero, is bounded
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
150554
proof that $f'$ is continuous at $a$
29154
$f$ is continuous and open implies $f$ injective
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
149407
Weak-to-weak continuous operator which is not norm-continuous
83461
Continuous iff composition with every linear functional is continuous
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes