Topology
2nd Edition
ISBN: 9780134689517
Author: Munkres, James R.
Publisher: Pearson,
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Chapter 2.17, Problem 6.1E
To determine
To prove:
The inclusion
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Name
Assume there is the following simplified grade book:
Homework Labs | Final Exam | Project
Avery
95
98
90
100
Blake
90
96
Carlos
83
79
Dax
55
30
228
92
95
79
90
65
60
Assume that the weights used to compute the final grades are homework 0.3, labs 0.2,
the final 0.35, and the project 0.15.
| Write an explicit formula to compute Avery's final grade using a single
inner product.
Write an explicit formula to compute everyone's final grade simultane-
ously using a single matrix-vector product.
1. Explicitly compute by hand (with work shown) the following Frobenius inner
products
00
4.56 3.12
(a) ((º º º). (156
(b)
10.9
-1
0
2)),
Fro
5')) Fro
Chapter 2 Solutions
Topology
Ch. 2.13 - Prob. 1ECh. 2.13 - Consider the nine topologies on the set X=a,b,c...Ch. 2.13 - Show that the collection Tc given in Example 4 of...Ch. 2.13 - a If {T} is a family of topologies on X, show that...Ch. 2.13 - Show that if A is a basis for a topology on X,...Ch. 2.13 - Show that the topologies of l and K are not...Ch. 2.13 - Consider the following topologies on : T1 = the...Ch. 2.13 - a Apply Lemma 13.2 to show that the countable...Ch. 2.16 - Show that if Y is a subspace of X, and A is a...Ch. 2.16 - If and are topologies on X and is strictly...
Ch. 2.16 - Consider the set Y=[1,1] as a subspace of .Which...Ch. 2.16 - A map f:XY is said to be an open map if for every...Ch. 2.16 - Let X and X denote a single set in the topologies ...Ch. 2.16 - Exercises Show that the countable collection...Ch. 2.16 - Prob. 7ECh. 2.16 - Exercises If L is a straight line in the plane,...Ch. 2.16 - Exercises Show that the dictionary order topology...Ch. 2.16 - Exercises Let I=[0,1]. Compare the product...Ch. 2.17 - Let C be a collection of subsets of the set X....Ch. 2.17 - Show that if A is closed in Y and Y is closed in...Ch. 2.17 - Show that if A is closed in X and B is closed in...Ch. 2.17 - Show that if U is open in X and A is closed in X,...Ch. 2.17 - Let X be an ordered set in the order topology....Ch. 2.17 - Prob. 6.1ECh. 2.17 - Prob. 6.2ECh. 2.17 - Let A, B, and A denote subsets of a space X. Prove...Ch. 2.17 - Prob. 7ECh. 2.17 - Let A, B, and A denote subsets of a space X....Ch. 2.17 - Let A, B, and A denote subsets of a space X....Ch. 2.17 - Let A, B, and A denote subsets of a space X....Ch. 2.17 - Let AX and BY. Show that in the space XY, AB=AB.Ch. 2.17 - Show that every order topology is Hausdorff.Ch. 2.17 - Show that the product of two Hausdorff spaces is...Ch. 2.17 - Show that a subspace of a Hausdorff space is...Ch. 2.17 - Show that X is Hausdorff if and only if the...Ch. 2.17 - Prob. 14ECh. 2.17 - Show the T1 axiom is equivalent to the condition...Ch. 2.17 - Prob. 16.1ECh. 2.17 - Consider the five topologies on given in Exercise...Ch. 2.17 - Consider the lower limit topology on and the...Ch. 2.17 - Prob. 19ECh. 2.18 - Prove that for functions f:, the definition of...Ch. 2.18 - Prob. 2ECh. 2.18 - Let X and X denote a single set in the two...Ch. 2.18 - Let X and X denote a single set in the two...Ch. 2.18 - Given x0X and y0Y, show that the maps f:XXY and...Ch. 2.18 - Show that subspace (a,b) of is homeomorphic with...Ch. 2.18 - Prob. 6ECh. 2.18 - (a) Suppose that f: is continuous from the right,...Ch. 2.18 - Let Y be an ordered set in the order topology. Let...Ch. 2.18 - Let {A} be a collection of subsets of X; let X=A....Ch. 2.18 - Let f:AB and g:CD be continuous functions. Let us...Ch. 2.18 - Prob. 11ECh. 2.19 - Prove Theorem 19.2. Theorem 19.2. Suppose the...Ch. 2.19 - Prove Theorem 19.3. Theorem 19.3. Let A be a...Ch. 2.19 - Prove Theorem 19.4. Theorem 19.4. If each space X...Ch. 2.19 - Show that (X1Xn1)Xn is homeomorphic with X1Xn.Ch. 2.19 - One of the implications stated in Theorem 19.6...Ch. 2.19 - Let be the subset of consisting of all sequences...Ch. 2.19 - Given sequences (a1,a2,...) and (b1,b2,...) of...Ch. 2.19 - Show that the choice axiom is equivalent to the...
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