# Axiom of choice and compactness.

I was addressing an inquiry lately that managed compactness as a whole topological rooms, and also just how compactness falls short to be equal with consecutive compactness unlike in metric spaces.

The only counter - instances that took place in my mind called for hefty use axiom of choice: well - getting and also Tychonoff is theory.

Can a person generate counter - instances of compactness not being equal with consecutive compactness without the usage axiom of choice? Or is it also feasible?

Many thanks for all the input beforehand.

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T. Eskin 2022-07-25 20:47:06

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