Connected and disconnected fields. (English) Zbl 0635.12019
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.
Reviewer: W.Wieşław
MSC:
| 12J99 | Topological fields |
| 54D05 | Connected and locally connected spaces (general aspects) |
| 54H13 | Topological fields, rings, etc. (topological aspects) |
| 54G05 | Extremally disconnected spaces, \(F\)-spaces, etc. |
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