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We define the minimum cardinarity of bases of a topology T is called the weight of T ,I want to know how to prove the weight of the cofinite topology T on ℝ is uncountable.

kuanglei
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    As @SoumikMukherjee rightly noticed, you will have better luck searching for cofinite topology not being second-countable, than for it having uncountable weight (which is the same thing). – Jakobian Mar 10 '24 at 15:48
  • you mean the fouth question?@SoumikMukherjee But I don't know what the meaning of "at the point" – kuanglei Mar 10 '24 at 16:30
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    @kuanglei No, the third question. Briefly, the character of a point $x$ is defined as the smallest cardinality of a local base at $x$. The character of the topological space is defined as the supremum over all the characters. A space is called 1st countable if its character is at most countable. Otoh, a space is called 2nd countable if its weight is at most countable. – Soumik Mukherjee Mar 10 '24 at 16:49
  • @SoumikMukherjeeThank you so much, I have done it. – kuanglei Mar 13 '24 at 01:55

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