# Tag: axiom-of-choice

## set theory – What are the Axiom of Choice and Axiom of Determinacy?

The Question : 109 people think this question is useful Would someone please explain: What does the Axiom of Choice mean, intuitively? What does the Axiom of Determinancy mean, intuitively, and how does it contradict the Axiom of Choice? as simple words as possible? From what I’ve gathered from the Wikipedia page, my understanding is

## set theory – Can you explain the “Axiom of choice” in simple terms?

The Question : 134 people think this question is useful As I’m sure many of you do, I read the XKCD webcomic regularly. The most recent one involves a joke about the Axiom of Choice, which I didn’t get. I went to Wikipedia to see what the Axiom of Choice is, but as often happens

## functional analysis – Does the open mapping theorem imply the Baire category theorem?

The Question : 220 people think this question is useful A nice observation by C.E. Blair1, 2, 3 shows that the Baire category theorem for complete metric spaces is equivalent to the axiom of (countable) dependent choice. On the other hand, the three classical consequences of the Baire category theorem in basic functional analysis — the