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JonSK
  • Member for 6 years, 7 months
  • Last seen more than 6 years ago
5 votes

Showing that $\{(x,y):x-y\ne 2\}$ in $\mathbb{R}^2$ is open

5 votes
Accepted

Proving that if $A$ is a closed set then $\bar{A} = A$

3 votes
Accepted

simple proof for principle of pigeons

2 votes

Show that $\underset{x\in X}{\sup}\left(\underset{y\in Y}{\sup}f(x,y)\right) = \underset{(x,y)\in X\times Y}{\sup} f(x,y)$

2 votes
Accepted

An example of a space that does not satisfies the 1º countability axiom

2 votes
Accepted

Homeomorphism between the Unit Disc and Complex Plane

2 votes
Accepted

Formal proof that (x,|x|) is not a smooth submanifold of $\mathbb{R}^2$

2 votes
Accepted

Show$d : x, y \in E \to \|x − y\|_E$ is a distance on $E$ and every open ball is the image of the unit ball under an affine map then check closure.

1 vote

Given a function $f: X \to Y$, if $X$ is compact, prove the graph $g = (x, f(x))$ is compact in $X\times Y$

1 vote

Show that a function is an embedding

1 vote

If $f: \mathbb{R} \rightarrow \mathbb{R}$ is continuous, show that the set of points fixed by $f$ is a closed subset of $\mathbb{R}$.

1 vote

Unique determination for the extension of $f: A \to Y$ into the closure of A (Munkres 18.13)

1 vote

Measure Theory on integrals

1 vote

Proof of $[0,1]~\text{disconnected}\implies(0,1)~\text{disconnected}$

1 vote
Accepted

Arbitrary basis of a separable metric space

1 vote
Accepted

Isometries of metric spaces $Z=X\cup (X\times\mathbb{R})$ (corrected)

0 votes

Induced topologies by Metric Spaces continuous

0 votes

How can I show that there cannot exist a homotopy from $\mathcal{C_1}$ to $\mathcal{C_2}$?

0 votes

Let $I = [0,1]$ and compare the following three topologies on $I^{2} = I \times I$.

0 votes

Sigma algebra question