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Apr
21
awarded  Popular Question
Apr
15
comment Can we prove that every real number is a limit of a sequence of rational numbers without Axiom of Choice?
@Carl Mummert [I am still notified if my name us typed correctly.] Suppose there are two members in this thread whose first name is Carl?
Apr
14
comment Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
@AsafKaragila [Pick an open cover, consider its projections, find a finite subcover for the first coordinate, then a finite subcover for the second coordinate.] Unfortunately it is not that simple. Please read Andres Caicedo's comment to my answer to this question.
Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
@AndresCaicedo A good point. By the way, why did you vote to close this question?
Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
@Carl Mummert [the issue is that you didn't do enough before asking the question.] How do you know that?
Apr
14
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
@Carl Mummert [If you had worked it out before asking, the entire question would have been unnecessary.] Answering one's own question is legitimate. Furthermore it can be useful for other members. Another point you seem to forget is that there are usually several or many solutions to a mathematical problem each of which might have its own merit. Just because I know one solution may not be the end of the case.
Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
answered Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
Apr
14
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
@AsafKaragila I edited the question. Does that satisfy you?
Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
@Carl Mummert [Please improve the question - as it stands, it shows no effort.] Please read my edit. If I'm not mistaken, I have proved it. In other words, I paid effort.
Apr
14
revised Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
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Apr
14
asked Construction of the field of real numbers within $ZF$
Apr
14
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
I posted a meta question asking the reason why this question was put on hold.
Apr
14
revised Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
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Apr
14
comment Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
@CarlMummert Would you please elaborate on your claim as an answer?