Connected and disconnected fields
The author summarizes the known results on connected and disconnected fields and adds some new results in this direction. He proposes a detailed classification of different kinds of connectedness of fields. Examples are sought of Hausdorff ring topologies on fields that are \((i)\quad arcwise\) connected; \((ii)\quad connected\) but not arcwise connected (just connected); \((iii)\quad totally\) disconnected but not ultraregular; \((iv)\quad ultraregular\) but not basically disconnected; \((v)\quad basically\) disconnected but neither a P-space nor extremally disconnected; \((vi)\quad P-spaces\); \((vii)\quad extremally\) disconnected. For a field with a ring topology, properties of F-zerosets are considered.
scientific article; zbMATH DE number 4033874
scientific article