23,498 reputation
11633
bio website at.yorku.ca/cgi-bin/bbqa
location Netherlands
age 44
visits member for 4 years
seen 28 mins ago

Got a PhD in topology in 98, now a cryptographer.


27m
comment Stuck on basics: How to prove that {subst($\alpha$,s)} is well defined?
If it's defined recursively, an inductive proof is often the way to go.
1h
answered Proving least upper bound property implies greatest lower bound property
2h
comment Proving least upper bound property implies greatest lower bound property
BTW, your $B$ example (from the last part) is not bounded below (in $S$, which is the point!). So we need not show that $B$ has an infimum to see that $S$ has the largest lower bound property .
2h
comment Proving least upper bound property implies greatest lower bound property
@Kevin $\sup(\emptyset) = \min(S)$ by definition. All elements of $S$ are upperbounds.
2h
comment Let X be a space with topology T, let U be the collection that U={(X\A)|A in T}
Hint for 1: the "only" difference between closed sets and open sets is that one is closed under all intersections/unions and the other under finite ones. $S3$ = ?
5h
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
@Tac-Tics this fact is not topological so I wanted to give a non-topological proof.
13h
comment The empty set as an Indexing set.
See also math.stackexchange.com/a/370201/4280
13h
answered The empty set as an Indexing set.
22h
comment Chinese remainder theorem other way around
8 and 125 have 1000 as a product, and don't have a common divisor. This is the only way to split $1000 = 2^3 5^3$ that way. Otherwise the Chinese remainder theorem does not apply.
22h
comment Finding $m$ largest numbers from union of $k$ sorted lists $A_1, A_2, \ldots, A_k$
quora.com/…
23h
answered Topology; Definition of the open ball and open sets confuses me
23h
comment Why separate the assignment function from the interpretation function?
Yes. You don't want to interpret your example formula as one where the relation can vary together with the $x$,$y$, $z$. You fix the relation, and then afterwards vary the variables. So you need to fix the model (i.e. the interpretation of relations, constants etc.) and interpret formulae within that fixed model. Afterwards you can talk about formulae that stay true even regardless of the model interpretation.
1d
comment Regular spaces, weight and dense subsets
Yes it does. And $|X| \le 2^{w(X)}$ as well.
1d
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
Thanks, edited it.
1d
revised Every sequence in $\mathbb{R}$ has a monotonic subsequence
edited body
1d
answered Every sequence in $\mathbb{R}$ has a monotonic subsequence
1d
comment Why separate the assignment function from the interpretation function?
The interpretation defines the model as a whole. Assignment applies to specific fomulae.
1d
comment Dimensions definition?
math.stackexchange.com/a/1076332/4280
1d
answered Conditions so that Lebesgue Covering Dimension and “Usual” Dimension are Equal
1d
comment At what conditions a compact metric space of covering dimension $n$ (on $\mathbb R^n$) is an n-manifold?
If you settle for non-isometric embeddings, $N = 2n$ will do and is optimal.