Katlus
Reputation
2,420
Next privilege 2,500 Rep.
Create tag synonyms
 Jan 23 revised How come this series could be well-defined? deleted 1 characters in body; added 1 characters in body; added 1 characters in body Jan 23 asked How come this series could be well-defined? Jan 21 comment Is there a clever way to avoid choice in Riesz Representation Theorem? Thank you Asaf. I skimmed it up, but now i'm a bit worried.. I'm enjoying mathematics without choice but this seems completely different way to develop measure theory from the usual. Should i study measure theory 'with choice' first then come back and study Borel Hierarchy? Or is it ok to study directly this paper you suggested? Jan 21 accepted Is there a clever way to avoid choice in Riesz Representation Theorem? Jan 20 asked Is there a clever way to avoid choice in Riesz Representation Theorem? Jan 18 answered How do i prove that this given set is open? Jan 18 asked How do i prove that this given set is open? Jan 17 comment What are 'weak' forms of Urysohn's lemma, which do not require choice? However, I'm not sure Urysohn's lemma holds for locally compact space. Is it provable? Jan 17 comment What are 'weak' forms of Urysohn's lemma, which do not require choice? @gnometorule I just spent my whole day to read the argument and whole references in the link related to Urysohn's Lemma, and it works fine without any choice! And more surprisingly, "If $X$ is a regular Hausdorff and second countable and $A,B$ are disjoint closed subsets, there exists a 'uniquely' defined continuous function $f:X\rightarrow [0,1]$ such that $f(A)\subset\{0\}$ and $f(B)\subset\{1\}$" is true in ZF Jan 17 comment What are 'weak' forms of Urysohn's lemma, which do not require choice? @Martin Yes, exactly. How do i call $d(x,A)$ then? Jan 17 comment What are 'weak' forms of Urysohn's lemma, which do not require choice? @gnometorule Are you even sure for the argument in the link? Otherwise i'm going to spend my whole day to check it. Jan 16 revised What are 'weak' forms of Urysohn's lemma, which do not require choice? added 76 characters in body Jan 16 asked What are 'weak' forms of Urysohn's lemma, which do not require choice? Jan 16 accepted How do i prove that $C_c(X)$ is a vector space? Jan 16 asked How do i prove that $C_c(X)$ is a vector space? Jan 16 comment What is your definition for neighborhood in topology? Would you please answer my comment above? Jan 16 comment What is your definition for neighborhood in topology? @Zhen I'm completely unfamiliar with the definition in wikipedia. Does the existence of a neighborhood (wikipedia definition) of $x$ gurantees the the existence of a open set containing $x$ then? Jan 16 accepted What is your definition for neighborhood in topology? Jan 16 asked What is your definition for neighborhood in topology? Jan 15 comment What is wrong in my proof? (Uniform convergence and Lebesgue integral) I want to make it clear. Is "$f$ is Lebesgue Integrable" same as saying "$f\in L^1(\mu)$"?