Corpus ID: 119635963

The normality and bounded growth of balleans

@article{Banakh2018TheNA,
  title={The normality and bounded growth of balleans},
  author={T. Banakh and I. Protasov},
  journal={arXiv: General Topology},
  year={2018}
}
By a ballean we understand a set $X$ endowed with a family of entourages which is a base of some coarse structure on $X$. Given two unbounded ballean $X,Y$ with normal product $X\times Y$, we prove that the balleans $X,Y$ have bounded growth and the bornology of $X\times Y$ has a linearly ordered base. A ballean $(X,\mathcal E_X)$ is defined to have bounded growth if there exists a function $G$ assigning to each point $x\in X$ a bounded subset $G[x]\subset X$ so that for any bounded set $B… Expand
7 Citations
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