Real Analysis
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Open, Closed and Compact SetsReal Analysis 2022. 8. 2. 11:20
1. a neighbourhood 2. Open set 3. Criterion of Closeness 4. Compact https://slideplayer.com/slide/13773591 Introduction to Real Analysis - ppt download Open cover Definition Let E be a subset of R. A collection of open subsets of R is an open cover of E if Alternative definition: The collection of open sets is an open cover of E if slideplayer.com https://www.youtube.com/watch?v=6CUr7dS1KeE (1) ..
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(Subseqeunces) Limit Superior and Limit InferiorReal Analysis 2022. 8. 1. 14:10
1. divergence, the improper accumulation value 2. limsup, liminf definition 3. limsup, liminf lemma - Because the sequence is monotonically decreasing and bounded, we also know that the limit is going to be the same thing as the infimum of sup s_k No matter how big number k is, the largest accumulation value is not changed. 4. limsup, liminf lemma 2 - 11/22/17 The third version of the limsup def..
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(Subsequences) Subsequences and accumulation valuesReal Analysis 2022. 8. 1. 05:44
1. Subsequence 2. Accumulation value, cluster point, limit point, partial limit Q. Do limits of subsequences exist? Bolzano-Weierstrass Theorem Q. What is the largest value in all limits of subsequences going to be? The Limit Superior Q. What is the smallest value in the set going to be? The Limit Inferior
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