9,292 reputation
12241
bio website jvanname.myweb.usf.edu
location Gotham, NY
age 25
visits member for 3 years
seen 2 days ago

I am interested in to varying degrees ordered sets, general topology, point-free topology, set-theory, universal algebra, and model theory. Most of my mathematics research involves dualities that are similar to Stone duality.


2d
awarded  Disciplined
Mar
25
comment Continuous image relation on topological spaces
The Rudin-Keisler ordering can be formulated in terms of continuous mappings between spaces. In particular, if $X,Y$ are discrete spaces, then each mapping $f:X\rightarrow Y$ extends uniquely to a continuous map $\overline{f}:\beta X\rightarrow\beta Y$ between the Stone-Cech compactifications. If $u\in\beta X,v\in\beta Y$, then $v\leq_{RK}u$ iff there is a continuous mapping $f:X\rightarrow Y$ such that $\overline{f}(u)=v$. Similarly, the Wadge heirarchy is another notion of reducibility by continuous mappings.
Mar
24
awarded  Nice Answer
Mar
24
answered Connectedness in the language of path-connectedness
Mar
21
comment What algebraic identities does the iteration of forcing operation satisfy?
Miha. I see. I will have to think about this some more and/or rewrite my comments.
Mar
21
revised What algebraic identities does the iteration of forcing operation satisfy?
added 111 characters in body
Mar
21
comment What algebraic identities does the iteration of forcing operation satisfy?
@Joel David Hamkins. I see. I attempted to specify that $\phi$ does respect isomorphisms in Boolean algebras, but I was missing a certain formula. Let me edit that.
Mar
21
comment What algebraic identities does the iteration of forcing operation satisfy?
Andreas Blass. I have added the requirement $ZFC\vdash\exists x\phi(x)$.
Mar
21
revised What algebraic identities does the iteration of forcing operation satisfy?
added 33 characters in body
Mar
21
asked What algebraic identities does the iteration of forcing operation satisfy?
Mar
20
awarded  Yearling
Mar
18
awarded  Enlightened
Mar
18
awarded  Nice Answer
Mar
18
comment Images of $\{0,1\}^\kappa$
I corrected the typos.
Mar
18
revised Images of $\{0,1\}^\kappa$
added 607 characters in body
Mar
18
revised Images of $\{0,1\}^\kappa$
edited tags
Mar
18
answered Images of $\{0,1\}^\kappa$
Mar
14
revised Critical topological spaces
added 992 characters in body
Mar
14
revised Critical topological spaces
added 992 characters in body
Mar
13
answered Critical topological spaces