New posts in metric-spaces

Metrizability of a compact Hausdorff space whose diagonal is a zero set

general-topology metric-spaces compactness separation-axioms

Walter rudin 9.32

analysis derivatives metric-spaces matrix-rank projection

A natural-looking distance formula

geometry metric-spaces

Showing that a totally bounded set is relatively compact (closure is compact)

analysis metric-spaces compactness cauchy-sequences

Showing the metric $\rho=\frac{d}{d+1} $ induces the same toplogy as $d$

general-topology metric-spaces

Sufficient condition to inscribe a polygon inside another one

metric-spaces euclidean-geometry polygons

Fixed Point Property for a special space?

general-topology metric-spaces fixed-point-theorems

What sorts of (sets of) equations are "approximately compatible" with the $2$-sphere?

general-topology logic metric-spaces universal-algebra

Metric independent definition of the derivative

differential-geometry metric-spaces stokes-theorem exterior-derivative

Prove that the following three metric space/subsequence boundedness conditions are equivalent.

real-analysis metric-spaces

Continuous functions of $(0,1)$ form a metric space

real-analysis metric-spaces

What is straight line?

metric-spaces definition philosophy geometry

Conjecture: the function $d(x, y):=\frac{||x-y||}{\max(||x||, ||y||)}$ is a distance

metric-spaces hilbert-spaces

Metric space and continuity

real-analysis convergence-divergence metric-spaces continuity

The distance function on a metric space

real-analysis general-topology metric-spaces uniform-continuity

Let $d(x,y)=|x-y|$, when does $|x-y|^p$ define a metric?

general-topology metric-spaces

Completeness of $\ell^2$ space

functional-analysis metric-spaces banach-spaces lp-spaces

Can we define any metric on $\Bbb{R^\omega}$ so that it represents a norm?

functional-analysis metric-spaces set-theory normed-spaces axiom-of-choice

Clopen subsets of a compact metric space

general-topology metric-spaces compactness

Does the metric $d(x,y)=||x-y||^p$ for $0<p<1$ induce the usual topology on $\mathbb{R}^n$?

real-analysis metric-spaces