19,213 reputation
11230
bio website at.yorku.ca/cgi-bin/bbqa
location Netherlands
age 44
visits member for 3 years, 9 months
seen yesterday

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


Aug
24
answered Cardinality of fibres of covering maps of connected spaces
Aug
23
comment Cardinality of fibres of covering maps of connected spaces
Show that the set $\{b \in B: |p^{-1}(b)|=k \}$ is open and closed when $p$ is a covering map.
Aug
21
answered Accumulation point in topological space problem
Aug
20
comment Accumulation point in topological space problem
What definition of subnet do you use? There are 3 different such notions.
Aug
20
comment Accumulation point in topological space problem
Should it not be: iff there exists a subnet that converges to $x$? That I can prove.
Aug
19
comment continuous function-constant
Look at hyperconnected and ultraconnected spaces. E.g the natural numbers in the upper or lower topology, e.g.
Aug
13
answered Continuous functions on compact Hausdorff space.
Aug
11
comment continuity in the strong topology implies continuity in the weak one
Ah, I did not know that convention
Aug
10
comment Connected Sets in Topology
@Maryam no set with more than one point is connected in the lower limit topology.
Aug
10
answered continuity in the strong topology implies continuity in the weak one
Aug
10
comment Connected Sets in Topology
Always good to ask, though. Self-study is tricky that way, as you cannot ask it in class.
Aug
10
answered Connected Sets in Topology
Aug
10
comment Non Archimedean field
@Sushil For Cauchy sequences to make sense, we need a metric on the field. So what metric are you using on the rational functions?
Aug
10
comment Is every dense subspace of a separable space separable?
Every open subset of a separable space is separable. It fails for closed sets (e.g. the antidiagonal in the Sorgenfrey plane). It also fails for dense sets, see the examples.
Aug
10
answered If $A\Delta B=C\Delta D$, must $A\Delta C=B\Delta D$?
Aug
10
awarded  metric-spaces
Aug
9
answered Is every dense subspace of a separable space separable?
Aug
9
comment Proof: Product Topology Question XxY
@DoanHoangLong what is your definition of the product topology?
Aug
9
comment Prove that: If $X$ is a topological space and $A$ and $B$ are two subsets of $X$ then,$Cl(A) \cup Cl(B) = Cl(A \cup B) $
If we know that $x$ is in the closure of $A \cup B$, then we know it is either in the closure of $A$ (and every neighbourhood intersects (at least) $A$) or in the closure of $B$ and every neighbourhood of $x$ intersects (at least) $B$. Of course it could always intersect both (and $x$ would even be in the closure of $A \cap B$), or sometimes intersect only one of them. But there is one of the two sets that neighbourhoods of $x$ always intersects, yes.
Aug
9
revised Prove that: If $X$ is a topological space and $A$ and $B$ are two subsets of $X$ then,$Cl(A) \cup Cl(B) = Cl(A \cup B) $
edited body