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Doing math.


Apr
10
answered Simply connectedness in $R^3$ with a spherical hole?
Apr
10
answered Homotopy on the unit circle
Apr
10
answered Is it possible to list $\mathbb{Q}$ so that the result set to be a monotonic sequence?
Apr
4
awarded  general-topology
Apr
3
comment Limit point compactness
Note that there are possibly subsets of $X$ that are neither open or closed. So "not closed" does not necessarily mean "open".
Mar
30
comment Does this limit give us the Cantor set?
When you say $\lim_{n\to a}x^{n}$, what exactly do you mean there? Under which metric are you limiting this sequence of sets? And what is $a$ in the limit?
Mar
19
comment Do open maps move isolated points to isolated points, in general?
Do you mean that $O$ is an open subset of $X$ instead of $A$? Because otherwise wouldn't we have $A\cap O=O$?
Mar
16
awarded  Nice Question
Mar
6
comment Using a contradiction to show something is not compact
@MPW: If you can take the continuity of determinant as obvious, then the set in question equals $\mathrm{det}^{-1}(\mathbb{R}\setminus\{0\})$ and is thus open. It should also be very elementary that $\mathbb{R}\setminus\{0\}$ is an open subset of $\mathbb{R}$.
Mar
5
answered Using a contradiction to show something is not compact
Feb
6
comment sum of two random variable
Random variables are functions and the sum of two random variables is just the sum of two functions in the usual sense.
Feb
5
comment Does addition have to be defined in metric spaces?
Why doesn't the finite discrete space have an addition or multiplication? It is equivalent with the axiom of choice that any non-empty set admits a group operation. The only question is whether this group action has any connection to the topology or not.
Jan
31
comment Show that sequence converges pointwise to a function that is not Riemann Integrable.
$C^{0}([a,b])$ might denote continuous functions $[0,1]\to \mathbb{R}$.
Jan
31
comment 'uniform approximation' of real in $[0,1]$
Are $n$ and $N$ the same number here? Also, what is $\varepsilon$?
Jan
29
comment How can a bounded subspace of the left order topology be compact?
Why is $(0,1)$ bounded? In other words, what notion of boundedness do you use? Especially since we are not looking at the standard topology on $\mathbb{R}$ with the standard metric to measure distances.
Jan
15
comment Convolution of integrable function with bounded function
What is the relationship of $H$ and $K$? Are they denoting the same function?
Jan
9
comment If $P(E_n) = 0$, then $P(\cup E_n) =0$
you probably have a typo there when using subadditivity: there shouldn't be a union after $\leq$, just the probabilities of the sets $E_{n}$.
Jan
6
awarded  Yearling
Jan
2
answered $G_\delta$ sets
Dec
20
comment Definition of functions on metric spaces.
Why would that cause any trouble? And which other way would you prefer to use to define a function?