I don't understand this weight fact at all

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In summary, the conversation discusses the concept of weight in a topological space and its relation to the cardinality of a basis. It is mentioned that there exists a basis with a cardinality less than the weight of the space, but it is clarified that the basis can also have a cardinality equal to the weight.
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1MileCrash
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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.
 

What is weight?

Weight is the measure of the force of gravity acting on an object. It is commonly measured in units of mass, such as kilograms or pounds.

How is weight different from mass?

Mass is the amount of matter in an object, while weight is the force exerted by gravity on that object. Mass is constant, but weight can change depending on the strength of gravity.

Why does weight vary on different planets?

Weight is directly proportional to the strength of gravity. Different planets have different masses and therefore different gravitational forces, resulting in varying weights for objects.

What is the difference between weight and density?

Weight is a measure of the force of gravity on an object, while density is a measure of how much mass is packed into a given volume. While weight can vary depending on gravity, density remains constant.

How is weight measured?

Weight is typically measured using a scale or balance that compares the gravitational force on an object to a known standard. It can also be calculated by multiplying an object's mass by the strength of gravity.

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