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For a general audience it can be interesting to know that uniform spaces are just one of two opposite generalizations of metric spaces. Measuring distances with the help of metric, we can be intereste …

It is well-known that each topological group $G$ carries (at least) four natural uniformities: the left uniformity $\mathcal L$, generated by the base $\{\{(x,y)\in G\times G:y\in xU\}:U\in\mathcal …

Mikhail Tkachenko informed me that the problem has a counterexample, constructed in Example 8.2.1 of his book with Arhangelskii. This example looks as follows. Consider the uncountable power $C_2^{\ …

A topological space $X$ is defined to have countable discrete cellularity if each discrete family of open subsets of $X$ is at most countable. A family $\mathcal F$ of subsets of a topological space …

For the Cantor starcase function $f:C\to[0,1]$ from the standard ternary Cantor set $C$ onto the interval $[0,1]$ and for the standard Euclidean metric $d$ on $C$ the quotient pseudometric $d_\sim$ is …