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Topology of \(\mathbb{R}\) and \(\mathbb{C}\)
Exercises
Correction
| A) Neighborhoods\(\virgule\) balls and convergence in \(\mathbb{K}\) | |
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| I) Open balls\(\virgule\) closed balls\(\virgule\) neighborhoods | |
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| 1) Computing balls and neighborhoods | Ex 1
Ex 2
Ex 3
Ex 4
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| II) Sequence convergence from the neighborhood viewpoint | |
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| 2) Verifying complex limits via Re/Im | Ex 5
Ex 6
Ex 7
Ex 8
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| III) Bolzano-Weierstrass in \(\mathbb{C}\) | |
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| 3) Applying iterated Bolzano-Weierstrass | Ex 9
Ex 10
Ex 11
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| B) Open sets\(\virgule\) closed sets\(\virgule\) interior and closure | |
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| I) Interior\(\virgule\) adherent points\(\virgule\) closure\(\virgule\) frontier | |
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| 4) Computing interior\(\virgule\) closure\(\virgule\) frontier | Ex 12
Ex 13
Ex 14
Ex 15
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| II) Open sets | |
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| 5) Proving a subset is open | Ex 16
Ex 17
Ex 18
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| III) Closed sets | |
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| 6) Proving a subset is closed | Ex 19
Ex 20
Ex 21
Ex 22
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| IV) Density | |
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| 7) Applying density | Ex 23
Ex 24
Ex 25
Ex 26
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