New posts in metric-spaces

Topological spaces vs. metric spaces

general-topology metric-spaces

How to show $\text{Given any sequence} (x^{(n)}) _{n\in\mathbb{N}}\text{ converges to } x \text{ in } (X ,|| •||), \text {X :finite dimensional NLS?}$

metric-spaces normed-spaces

French Railroad Metric/Topology

continuity metric-spaces

Proof that every metric space is normal

general-topology metric-spaces separation-axioms

How does a metric tensor describe geometry on a manifold?

differential-geometry metric-spaces riemannian-geometry

$C^1[a,b]$ is closed in $C[a,b]$

general-topology metric-spaces

Is this kind of space metrizable?

general-topology metric-spaces examples-counterexamples compactness

Consider $Y = \mathbb{N} \cup \{ \infty\}$ and $X = \{ \frac{1}{n}\mid n \in \Bbb N\} \cup \{0\}$

continuity metric-spaces

When is a Lipschitz homeomorphism of metric spaces bi-Lipschitz?

general-topology metric-spaces

Must compact bijections be continuous?

real-analysis general-topology continuity metric-spaces compactness

$d(x,y) = |f(x) - f(y)|$ on $\mathbb{R}$

metric-spaces compactness complete-spaces

Prob. 11, Chap. 4 in Baby Rudin: uniformly continuous extension from a dense subset to the entire space

real-analysis analysis metric-spaces cauchy-sequences uniform-continuity

$|f(x)-f(y)|\le(x-y)^2$ without gaplessness

real-analysis general-topology inequality metric-spaces

Proving a metric induces the product topology

general-topology metric-spaces proof-verification

Long proof of equivalence of subspace and metric topology

general-topology metric-spaces

Compact subset of an open set

general-topology functional-analysis metric-spaces descriptive-set-theory

pointwise limit on a complete metric space

general-topology functional-analysis metric-spaces continuity

What does the Pythagorean Theorem really prove?

soft-question metric-spaces

Does continuity of $f$ imply $f^{-1}(\bar A)\subset\overline{f^{-1}(A)}$?

general-topology metric-spaces proof-writing continuity examples-counterexamples

$\langle\mathbb{R},d\rangle$ is not separable [duplicate]

general-topology metric-spaces