6. Continuous functions

Notes

• Complete lecture notes
• Blank lecture notes

Videos

Part 1 (pages 51-53)

Part 2 (pages 54-55)

Part 3 (pages 56-57)

Part 4 (pages 58-59)

Page links

• Page 51: Continuous functions and closed sets.
• Page 52: Continuous functions and sequences in metric spaces.
• Page 53: Continuous functions and sequences in topological spaces.
• Page 54: Composition of continuous functions. Open pasting lemma.
• Page 55: Closed pasting lemma.
• Page 56: Homeomorphisms: definition, basic properties.
• Page 57: Equivalent definitions of a homeomorphism.
• Page 58: Homeomorphic spaces. Examples.
• Page 59: Stereographic projection.

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