Reputation
4,745
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
2 11 34
Impact
~60k people reached

May
17
comment Axiom of choice and compactness.
@AsafKaragila: Thanks. What would you suggest?
May
17
comment Axiom of choice and compactness.
Alright, thanks a lot Asaf. I have both books in my hands now, can't wait to study them later today. My knowledge of set theory is not in a very high level, but I'm getting there slowly :-)
May
16
comment Axiom of choice and compactness.
Thanks; that link contains some nice discussions.
May
16
accepted Axiom of choice and compactness.
May
16
comment Axiom of choice and compactness.
Thanks for the excellent reply. I was aware of compactness being equiv with ultrafilter compactness in ZFC, but I will look up Herrlich's material for sure. The infinite Dedekind-finite set sounds very interesting. What do you think would be the best source to look it up from?
May
16
asked Axiom of choice and compactness.
May
16
revised Dealing with Tychonoff's Theorem.
deleted 4 characters in body
May
16
answered Dealing with Tychonoff's Theorem.
May
16
comment Dealing with Tychonoff's Theorem.
What do you mean by Heine-Borel definition of compactness?
May
16
answered Cantor set: Lebesgue measure and uncountability
May
16
comment A metric space problem
By choosing $A=B$ we see that it does not imply. Did you mean instead that does it imply $A\cap B\neq \emptyset$?
May
16
revised Connection of ideas of Measuring to the Measure theory .
added 27 characters in body
May
16
answered Connection of ideas of Measuring to the Measure theory .
May
16
comment What does a simple function actually mean?
By the way, a simple function is continuous iff $\partial A_{i}=\emptyset$ for all $i$, so they can represent other continuous functions than constants depending on the underlying topology. In $\mathbb{R}^{n}$ and Euclidean topology you're right though, since the only sets without boundary are $\mathbb{R}^{n}$ itself and $\emptyset$.
May
16
answered What does a simple function actually mean?
May
16
revised one more clock related challenge!
added latex symboling.
May
16
suggested approved edit on one more clock related challenge!
May
16
revised Find volume of a revolved solid by integrating wedges.
Corrected latex symboling
May
16
suggested approved edit on Find volume of a revolved solid by integrating wedges.
May
16
comment Condition for an interval being contained in a subset of $\mathbb{R}$
The terminology that you used works fine :-) About endpoints, do you mean 'endpoints' of $A$? In that case they may not exist or make sense if $A$ is unbounded or if $A$ is very messy. There is a notion of 'closure' of a set, which you may want to check out unless you're already familiar with it. Speaking of endpoints of an interval is fine though.