Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Confidence Intervals
When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…
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Could you explain how to show 3.3 in detail? Thank you!

**Theorem 3.3.** Suppose \( X \) is a set and \( \mathcal{B} \) is a collection of subsets of \( X \). Then \( \mathcal{B} \) is a basis for some topology on \( X \) if and only if 1. Each point of \( X \) is in some element of \( \mathcal{B} \), and 2. If \( U \) and \( V \) are sets in \( \mathcal{B} \) and \( p \) is a point in \( U \cap V \), there is a set \( W \) in \( \mathcal{B} \) such that \( p \in W \subseteq (U \cap V) \).
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Transcribed Image Text:**Theorem 3.3.** Suppose \( X \) is a set and \( \mathcal{B} \) is a collection of subsets of \( X \). Then \( \mathcal{B} \) is a basis for some topology on \( X \) if and only if 1. Each point of \( X \) is in some element of \( \mathcal{B} \), and 2. If \( U \) and \( V \) are sets in \( \mathcal{B} \) and \( p \) is a point in \( U \cap V \), there is a set \( W \) in \( \mathcal{B} \) such that \( p \in W \subseteq (U \cap V) \).
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