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Aug
10
comment Product topology help required.
Let's put it this way: there are almost certainly many different ways to put a topology on $G\times G$. I'm guessing that there is a specific one that you are intended to show actually is a topology. Perhaps you could edit your question to include its description.
Aug
10
comment Product topology help required.
What's the proposed topology that you are putting on $G \times G$?
Aug
10
revised Every open set in the real line is the countable union of disjoint intervals
edited title
Aug
10
comment Every open set in the real line is the countable union of disjoint intervals
You should be a bit more careful in phrasing things. Not every separable space is second-countable (or even hereditarily Lindelöf, which is what you are using). (For example, the Niemytzki/Moore plane.) Although in metric spaces separability and second countability (and Lindelöfness, etc.) coincide.
Aug
10
revised Every open set in the real line is the countable union of disjoint intervals
reel ≠ real
Aug
10
comment Proving $\frac{1}{1\cdot3} + \frac{1}{2\cdot4} + \cdots + \frac{1}{n\cdot(n+2)} = \frac{3}{4} - \frac{(2n+3)}{2(n+1)(n+2)}$ by induction for $n\geq 1$
I have attempted to clean this up by introducing MathJax. Please check it over to ensure that I haven't inadvertantly introduced any errors. For more information about typesetting mathematics here please see our MathJax basic tutorial and quick reference.
Aug
10
revised Proving $\frac{1}{1\cdot3} + \frac{1}{2\cdot4} + \cdots + \frac{1}{n\cdot(n+2)} = \frac{3}{4} - \frac{(2n+3)}{2(n+1)(n+2)}$ by induction for $n\geq 1$
MathJaxified
Aug
9
comment Is there a general solution to the water-bucket logic problem?
Then don't give a short answer: posts here can be up to 30,000 characters long.
Aug
9
comment Is there a general solution to the water-bucket logic problem?
While information at these links may theoretically answer the question, it would be preferable to include the essential parts of the answer here, and provide the links for reference.
Aug
8
reviewed Edit Characterizing the continuous functions from $\mathbb{N}$ with the cofinite topology to $\mathbb{R}$
Aug
8
revised Characterizing the continuous functions from $\mathbb{N}$ with the cofinite topology to $\mathbb{R}$
math symbol
Aug
8
revised There are infinitely many monomial orders
incorporating all answers from this user here.
Aug
7
reviewed Reject Has the Collatz Conjecture been proven to be unprovable?
Aug
7
reviewed Approve Show that there's a minimum spanning tree if all edges have different costs
Aug
7
revised Topological properties of $[0,\omega_1)$ without choice.
pre-comment-deleting edit
Aug
7
comment Example of a nowhere dense subset of a metric space.
In topology, an isolated point is one whose singleton is open. You appear to be using this term incorrectly.
Aug
6
revised Two Point Stone-Cech Compactification of an uncountable space
Mainly, putting info from my comment into answer (and then I can delete the comment).
Aug
6
comment Two Point Stone-Cech Compactification of an uncountable space
This space is homeomorphic to $[0,\omega_1) \times 2$.
Aug
6
revised Does $M \otimes_R N = 0$ for a non-unital ring $R$ if there are ideals $I,J \lhd R$ such that $MI+JN = 0$ and $I+J = R$?
added 3 characters in body; edited tags; edited title
Aug
6
comment Is the following topological space separable?
It's not really that $C_2$ is an uncountable discrete subspace (the Niemytzki/Moore plane has an uncountable discrete subspace, but is still separable), but that every point in $C_2$ is isolated (i.e., the singleton $\{x\}$ is open).