 11.2.1: Exhibit an open cover of the interval (1, 2] that has no finite sub...
 11.2.2: Exhibit an open cover of N that has no finite subcover.
 11.2.3: Exhibit an open cover of the set {I/ n: n e N}that has no finite su...
 11.2.4: Prove, using Definition 11.2.2, that if F is a closed subset of a c...
 11.2.5: Prove, using Definition 11.2.2, that if K1and K2 are compact sets i...
 11.2.6: Use the HeineBorel Theorem to prove the following version of the B...
 11.2.7: Find an infinite collection {Kn : n E N} of compact sets in JRsuch ...
 11.2.8: Prove that the intersection of an arbitrary collection of compact s...
 11.2.9: Let (Kn : n E N) be a sequence of nonempty compact sets in JRsuch t...
 11.2.10: Let K :f:0 be a compact set in IR.Show that inf K and sup K exist a...
 11.2.11: Let K :f: 0 be compactin IRand let e E JR.Prove that there exists a...
 11.2.12: Let K :f:0 be compact in JRand let e E IR.Prove that there exists a...
 11.2.13: Use the notion of compactness to give an alternative proof of Exerc...
 11.2.14: If K, and K2 are disjoint nonempty compact sets, show that there ex...
 11.2.15: Give an example of disjoint closed sets Fl' F2 such that 0 = inf{lx...
Solutions for Chapter 11.2: Compact Sets
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 11.2: Compact Sets
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 15 problems in chapter 11.2: Compact Sets have been answered, more than 9591 students have viewed full stepbystep solutions from this chapter. Chapter 11.2: Compact Sets includes 15 full stepbystep solutions.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Directed distance
See Polar coordinates.

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Inductive step
See Mathematical induction.

Multiplicative identity for matrices
See Identity matrix

Normal distribution
A distribution of data shaped like the normal curve.

Onetoone rule of exponents
x = y if and only if bx = by.

Parameter
See Parametric equations.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Range of a function
The set of all output values corresponding to elements in the domain.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Rose curve
A graph of a polar equation or r = a cos nu.

Slopeintercept form (of a line)
y = mx + b

xaxis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.

Yscl
The scale of the tick marks on the yaxis in a viewing window.