New posts in Normed Spaces

Prove that $\Vert\cdot \Vert^2:X\to \Bbb{R},$ where $X$ is a vector space, is convex

Reason for the term "smooth"

Proving that $S=\{ x \in (X,\| \cdot \|) : \|x\| =1 \}$ is a closed set.

Show that $f_n \to f$ over $\| \cdot \|_\infty$ implies $f_n \to f$ over $\| \cdot \|_2$ and is $(C[a,b], \|\cdot\|_2)$ Banach?

When does an inner product induce a norm?

Is the distance between two elements of a normed vector space at least the distance between their projections on the unit ball?

Properties of $\{x\in X\mid f(x)=||f||\}$

Relation between metric spaces, normed vector spaces, and inner product space.

Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space

Bounded linear transformation definition clarification