New posts in metric-spaces

Compact metric space group $Iso(X,d)$ is also compact

general-topology metric-spaces compactness

Finding a metric to make a certain curve a circle

differential-geometry metric-spaces differential-topology circles

Is this proof that all metric spaces are Hausdorff spaces correct?

general-topology metric-spaces proof-verification

Every 1-Lipschitz function in the closed unit ball has a fixed point

metric-spaces lipschitz-functions banach-fixed-point

How to show that disjoint closed sets have disjoint open supersets?

general-topology metric-spaces

Open set in a metric space is union of closed sets

Why the weak topology is never metrizable?

general-topology functional-analysis metric-spaces

Is total boundedness a topological property?

general-topology metric-spaces examples-counterexamples

Bijective local isometry to global isometry

differential-geometry metric-spaces differential-topology metric-geometry

Proof that the closure of $S$ is the set of all limits of convergent sequences in $S$

general-topology metric-spaces solution-verification

Proper inclusion between open ball, closure of open ball and the closed ball in a metric space

Characterization of the Subsets of Euclidean Space which are Homeomorphic to the Space Itself

general-topology metric-spaces

A is a subset of a metric space under given conditions. Prove there is a $y \in A$ that minimizes the distance from $x$ to elements of $A$

real-analysis metric-spaces

The set of irrational numbers is not a $F_{\sigma}$ set.

general-topology metric-spaces

Two proper subsets of the real numbers, $A$ and $B$, that have the following conditions: $A$ and $B$ are closed, $A \cap B$ is empty, +1

real-analysis metric-spaces

Any ball is connected?

general-topology metric-spaces compactness connectedness

Proving completeness of Nikodym Metric

real-analysis measure-theory metric-spaces cauchy-sequences

Is the Empty metric space, complete?

A continuous function that maps closed unit square to the unit open square

real-analysis general-topology continuity metric-spaces solution-verification

Characterisation of uniformly continuous function

general-topology metric-spaces uniform-continuity