- #1
de_brook
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An open base {B_i} for a topological space X is the class of open sets in X in which any open set in X is the union of sets in {B_i}.
Please consider the following and tell me if i am wrong
observation
An open cover in X is a subclass of some given open base for X. This then should imply that an open cover for X is a basic open cover contained in some given open base.This is because of the definition above and an open cover is a class of open sets whose union contains X
conclusion
Every open cover for a topological space X is a basic opencover. i am saying that an open cover must be contained in some given open base
Please consider the following and tell me if i am wrong
observation
An open cover in X is a subclass of some given open base for X. This then should imply that an open cover for X is a basic open cover contained in some given open base.This is because of the definition above and an open cover is a class of open sets whose union contains X
conclusion
Every open cover for a topological space X is a basic opencover. i am saying that an open cover must be contained in some given open base