I don't understand this weight fact at all

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The discussion centers on the concept of weight in topological spaces, specifically addressing the definition of weight as the minimum cardinality of a basis for a topological space T. Participants clarify that while the statement regarding the existence of a basis B' with cardinality less than or equal to the weight is technically correct, it could be more precise by stating that |B'| should equal w(X). This highlights a common confusion in understanding the nuances of topological bases and their cardinalities.

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http://en.wikipedia.org/wiki/Topological_basis#Weight_and_character

The 4th bullet says that if B is a basis for a top. space T, there is a basis B' that has a cardinality less than the weight of the space, but right before, the weight was defined to be the minimum cardinality of a basis.. :confused:
 
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Well, it says less than or equal, so technically it's still a correct statement, but I agree it should say |B'| = w(X) as far as I can tell.
 
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Office_Shredder said:
Well, it says less than or equal, so technically it's still a correct statement, but I agree it should say |B'| = w(X) as far as I can tell.

Oh OK! Thank you! I thought I was just in over my head.
 

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