hwk1 - Math 31BH - Homework 1. Due January 11. Part I. From...

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Math 31BH - Homework 1. Due January 11. Part I. From the textbook solve the following problems: 1. ( Monday ) Problem 1 . 5 . 1 , 1 . 5 . 2 , 1 . 5 . 3 . 2. ( Wednesday-Friday ) Problem 1 . 5 . 14 (a) (b), 1 . 5 . 19 , 1 . 5 . 21 (a) (c) (e). Part II. EC0. Problem 1 . 5 . 24 . EC1. ( Monday. Extra credit. Preview of Math 190, Topology . ) In this problem, we ex- tend the notion of open sets to more general sets, which may not be subsets of R n . Consider a set X and let T be a collection of subsets of X . We assume that the following properties are satisﬁed: (i) and X are members of T , (ii) union of members of T (which, recall, are subsets of X ) is still a member of T , (iii) ﬁnite intersection of members of T is still a member of T . A set X together with a collection of subsets T as above is said to be a topological space. T is referred to as the topology of X . The members of T are called the open sets of the topology. For instance, X = R n

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This note was uploaded on 03/28/2011 for the course MATH 31B taught by Professor Dragosoprea during the Winter '11 term at UCSD.

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hwk1 - Math 31BH - Homework 1. Due January 11. Part I. From...

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