- #1
dumb_curiosity
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In all the topology textbooks I used in school, the open set axoims specified 4 conditions on a set S:
(i) S is open
(ii) empty set is open
(iii) arbitrary union of open sets is open
(iv) finite intersection of open sets is openI noticed on proofwiki, that (ii) is omitted. I was curious if anyone might be able to tell me why this is.
https://proofwiki.org/wiki/Definition:Open_Set_Axioms
Is it wrong, or does (ii) just follow from the other axioms in a way I don't see?
(i) S is open
(ii) empty set is open
(iii) arbitrary union of open sets is open
(iv) finite intersection of open sets is openI noticed on proofwiki, that (ii) is omitted. I was curious if anyone might be able to tell me why this is.
https://proofwiki.org/wiki/Definition:Open_Set_Axioms
Is it wrong, or does (ii) just follow from the other axioms in a way I don't see?