Week 7; 6.3-7.1 Flashcards
1
Q
Define a contraction T from a metric space (X,d) to itself
A
2
Q
Contraction Mapping Theorem
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3
Q
Prove contraction mapping theorem
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4
Q
Error estimate
A
Where 6.20’is contraction mapping theorem
5
Q
Lipschitz condition
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6
Q
Picard Lindelof theorem
A
7
Q
Define interval I € R
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8
Q
A topological space (X, τ) is disconnected if
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9
Q
Equivalence of connectivity in topological space
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10
Q
Prove
A
11
Q
Define Clopen
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12
Q
Prove
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13
Q
Prove
A
14
Q
Quick way to check if S€X is connected
A
7.9: suppose that (X, τ) admits a non trivial clopen set A in X, then X is disconnected
15
Q
Prove
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