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| ``Re: topological field''
by djao on 2002-06-09 00:22:57 |
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| I am not sure. This is one item that I will have to investigate further.
For starters, continuity at 0 cannot be expected at all: x -> 1/x is almost never continuous at 0, yet we would like fields such as R and C to be topological fields.
The books that I have looked at do not specify in the definition that multiplicative inverse or additive inverse operations have to be continuous in a topological field or ring. Unfortunately they also do not address the issue of whether such continuity is automatically implied by the definition or not.
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