HelmutKnaust at 15:48, 14 October 2025

2025-10-14T15:48:08Z

HelmutKnaust: Created page with "'''Problem 16.''' Show: If $X\subseteq \mathbb{R}$ is both open and closed, then $X=\mathbb{R}$ or $X=\emptyset$. '''Problem 17.''' Exercise 3.2.7. '''Problem 18.''' Exercis..."

2025-10-14T15:46:00Z

Created page with "'''Problem 16.''' Show: If $X\subseteq \mathbb{R}$ is both open and closed, then $X=\mathbb{R}$ or $X=\emptyset$. '''Problem 17.''' Exercise 3.2.7. '''Problem 18.''' Exercis..."

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'''Problem 16.''' Show: If $X\subseteq \mathbb{R}$ is both open and closed, then $X=\mathbb{R}$ or $X=\emptyset$.

'''Problem 17.''' Exercise 3.2.7.

'''Problem 18.''' Exercise 3.2.14.

'''Problem 19.''' Consider the following sets:
\[A=\left\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4}\ldots\right\},\quad B=\left\{1,\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}\ldots\right\}, \quad C=\mathbb{Q}\cap[0,1]\]
For the sets that are compact, explain why. For the other ones, show that they have an open cover without finite subcover.

'''Problem 20.''' Exercise 3.4.6.

@@ Line 3: / Line 3: @@
 '''Problem 17.''' Exercise 3.2.7.
-'''Problem 18.''' Exercise 3.2.14.
+'''Problem 18.''' Exercise 3.2.15.
 '''Problem 19.''' Consider the following sets:

CRN 10459: HW 4 - Revision history

HelmutKnaust at 15:48, 14 October 2025

HelmutKnaust: Created page with "'''Problem 16.''' Show: If $X\subseteq \mathbb{R}$ is both open and closed, then $X=\mathbb{R}$ or $X=\emptyset$. '''Problem 17.''' Exercise 3.2.7. '''Problem 18.''' Exercis..."