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New posts in Metric Spaces
Prove that $U=\{x \in X\mid d(x,A)<d(x,B)\}$ is open when $A$ and $B$ are disjoint
May 06, 2021
If a collection of closed sets of arbitrary cardinality in a metric space has empty intersection, does some countable subcollection?
May 06, 2021
Hölder exponents greater than 1 imply function to be constant?
May 05, 2021
Show that the two norms in $E=\left\{f\in \mathcal{C}^1[0,1]:f(0)=0\right\}$ are equivalent?
May 05, 2021
If every sequence $(x_{n}) \subset X$ and $(\lambda_{n}) \subset \mathbb{R}$ we have $\lim \lambda_{n}x_{n} = 0$, then $X$ is bounded
May 05, 2021
Is a set bounded in every metric for a uniformity bounded in the uniformity?
May 05, 2021
If $d(x,y)$ is a metric on $X$, then $d'(x,y)=\frac{d(x,y)}{1 + d(x,y)}$ and $d(x,y)$ generates the same topology.
May 05, 2021
Example of a metric space where diameter of a ball is not equal twice the radius
May 05, 2021
How is the discrete metric continuous?
May 05, 2021
What sequences are Cauchy in all metrics for a given topology?
May 05, 2021
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