bio  website  

location  
age  24  
visits  member for  5 years 
seen  22 mins ago  
stats  profile views  11,696 
7h

reviewed  Close About freeness of modules over the coordinate ring of an affine variety 
1d

answered  Is every polynomial ring over any field regular? 
2d

comment 
“Nice” functions on infinitedimensional space of germs of continuous functions at a point
Can you even construct any linear functional on germs of continuous functions (besides multiples of evaluation at the point) without the axiom of choice? 
Oct 14 
comment 
Connected graph as connected space
The closure of any connected set is connected. 
Oct 12 
comment 
Connected graph as connected space
Any compactification of a connected space is connected. 
Oct 9 
comment 
Classification of rings satisfying $a^4=a$
@MartinBrandenburg: It is a Stone space if you topologize it based on $\mathbb{F}_4$ being discrete, rather than only $\{0\}$ being closed. 
Oct 7 
awarded  Nice Answer 
Oct 6 
awarded  Yearling 
Oct 1 
answered  Standard homology result on double complexes 
Sep 29 
comment 
What is the most useful nonexisting object of your field?
@AndréHenriques: Actually, it has $2^8$ elements. But you are correct that free complete Boolean algebras on finite sets exist (and are the same as free Boolean algebras). Free complete Boolean algebras on infinite sets do not exist. 
Sep 29 
reviewed  Looks OK What is the most useful nonexisting object of your field? 
Sep 23 
comment 
A simple example of a ring that is an $A$module but not an $A$algebra?
I'm not sure why you say $\mathbb{R}$ is a $\mathbb{C}$vector space but not a $\mathbb{C}$algebra; any embedding of $\mathbb{C}$ in $\mathbb{R}$ makes $\mathbb{R}$ a $\mathbb{C}$algebra. In your situation, $B$ will be an $A$algebra iff the action of $A$ on $B$ commutes with the action of $B$ on itself. Equivalently, $B$ is an $A$algebra iff the action of $a\in A$ coincides with multiplication by $a\cdot 1_B$ in the ring structure of $B$. 
Sep 9 
answered  Completion of the set of subsets with half volume. 
Sep 4 
awarded  Enlightened 
Sep 4 
awarded  Nice Answer 
Sep 3 
answered  Haar Measure on Locally Compact Semigroups 
Sep 2 
revised 
Is there a straightedge and compass construction of incommensurables in the hyperbolic plane?
edited tags 
Sep 1 
revised 
Group structure on an arbitrary completely regular topological space that makes $(x,y)\mapsto xy^{1}$ continuous at $(1,1)$
improved title 
Aug 27 
comment 
Clutching functions and Classifying maps
The clutching function correspondence gives you one way of constructing an equivalence $G\simeq \Omega BG$, and you are asking whether that equivalence is the same as the equivalence $G\simeq \Omega BG$. But this is impossible to answer without specifying how the latter equivalence is constructed. 
Aug 24 
comment 
Continuous relations?
@JoonasIlmavirta: That definition will give you closed relations, which are not very wellbehaved other than being symmetric in $X$ and $Y$. They are not closed under composition and include functions that are not continuous as functions. If you replace $K$ by $Y$ (so you are looking locally only on $X$), you get my definition of continuity (since it is local on the domain). 