nLab
archimedean protoring

Contents

Contents

Definition

A protoring MM is an archimedean protoring if for all terms a,b,c,dMa, b, c, d \in M, c<dc \lt d implies that there exists a positive natural number n +n \in \mathbb{N}_+ such that

b+ i=1 nc<a+ i=1 ndb + \sum_{i=1}^n c \lt a + \sum_{i=1}^n d

where

i=1 ()(): +×MM\sum_{i=1}^{(-)} (-):\mathbb{N}_+ \times M \to M

is the canonical left non-unital +\mathbb{N}_+-action for commutative semigroups? defined inductively by

i=1 1cc\sum_{i=1}^{1} c \coloneqq c
i=1 n+1cc+ i=1 n\sum_{i=1}^{n + 1} c \coloneqq c + \sum_{i=1}^{n}

See also

Examples

References

  • Davorin Lešnik, Synthetic Topology and Constructive Metric Spaces, (arxiv:2104.10399)

Created on May 12, 2022 at 08:27:57. See the history of this page for a list of all contributions to it.