• Title: Continuous Images of Compact Sets are Compact

• Series: Real Analysis

• Chapter: Continuous Functions

• YouTube-Title: Real Analysis 30 | Continuous Images of Compact Sets are Compact

• Bright video: https://youtu.be/6VWTG4wlRoA

• Dark video: https://youtu.be/WdDozI8S8mU

• Subtitle on GitHub: ra30_sub_eng.srt missing

• Timestamps (n/a)
• Subtitle in English (n/a)
• Quiz Content

Q1: Let $f: A \rightarrow \mathbb{R}$ be continuous. Which statement is not correct in general?

A1: If $A \subseteq \mathbb{R}$ is compact, then $f[A] \subseteq \mathbb{R}$ is compact.

A2: If $A \subseteq \mathbb{R}$ is bounded, then $f[A] \subseteq \mathbb{R}$ is bounded.

A3: If $A \subseteq \mathbb{R}$ is finite, then $f[A] \subseteq \mathbb{R}$ is finite.

Q2: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be continuous. Does the maximum of $f$ always exist?

A1: Yes!

A2: No!

Q3: Let $f: [0,1] \rightarrow \mathbb{R}$ be continuous. Does the maximum of $f$ always exist?

A1: Yes!

A2: No!

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