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 Yearling
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Mar
9
comment What is the predual of $L^1$
I think $K$ also needs to be Hausdorff no?
Feb
25
comment Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]
Ok thanks for clearing that up.
Feb
24
comment If $R=K[X]/(X^n)$, can represent any element as polynomial with degree $<n$
When you quotient by $(X^n)$ you're effectively saying any time you see $X^n$ you can replace the term with 0. So all terms of degree $\geq n$ will vanish.
Feb
24
comment Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]
What does "R is ccc" mean?
Feb
24
answered Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]
Feb
19
awarded  Yearling
Feb
19
awarded  Scholar
Feb
19
comment Are countably infinite, compact, Hausdorff spaces necessarily second countable?
This is interesting. I didn't know that there was such a complete classification for these spaces. I'll have to do some reading up on the Sierpinski-Mazurkiewicz theorem. Thanks!
Feb
19
accepted Are countably infinite, compact, Hausdorff spaces necessarily second countable?
Feb
19
revised If the sequence $a_n$ converges to $1$ then $a_{n+1}+\frac{1}{n}$ also converges to $1$
minor
Feb
19
answered If the sequence $a_n$ converges to $1$ then $a_{n+1}+\frac{1}{n}$ also converges to $1$
Feb
18
asked Are countably infinite, compact, Hausdorff spaces necessarily second countable?
Dec
17
awarded  Caucus
Sep
29
comment Does this graph operation have a name? Subgraph join?
The motivation behind naming it a "subgraph join" was that the definition is similar to that of a graph join (second definition at this link en.wikipedia.org/wiki/Graph_operations#Binary_operations), nevertheless what you said is a good point I'll keep in mind.
Sep
27
awarded  Student
Sep
27
comment Decimal expansion of a Cauchy sequence
This is pretty close, but I would specifically like to have $b_n$ represent decimal truncations of $a=\lim_{n\to\infty} a_n$. Also sorry for the really late response.
Sep
27
revised Decimal expansion of a Cauchy sequence
clarified the property that $b_n$ was supposed to have.
Sep
27
comment Does this graph operation have a name? Subgraph join?
In the second bullet I specify that the edge set is in general not just the union of the edge sets of A and B. For example if I have the the square $C_4$ and A,B,C,D are the subgraphs corresponding to each of the four vertices in clockwise order, then $A+B$ has 1 edge but $A+C=A\cup C$ and so has no edges.
Sep
27
revised Decimal expansion of a Cauchy sequence
Clarified what I meant by "determining an equivalent Cauchy sequence which corresponds to a decimal expansion"
Sep
27
revised Does this graph operation have a name? Subgraph join?
Grammer and notation clean-up