EBK INTERMEDIATE ALGEBRA
12th Edition
ISBN: 8220100802867
Author: BITTINGER
Publisher: PEARSON
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Textbook Question
Chapter A, Problem 33ES
c Compute and simplify.
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Q1lal Let X be an arbitrary infinite set and let r the family of all subsets
F of X which do not contain a particular point x, EX and the
complements F of all finite subsets F of X show that (X.r) is a topology.
bl The nbhd system N(x) at x in a topological space X has the following
properties
NO- N(x) for any xX
N1- If N EN(x) then x€N
N2- If NEN(x), NCM then MeN(x)
N3- If NEN(x), MEN(x) then NOMEN(x)
N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any
уем
Show that there exist a unique topology τ on X.
Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a
topology on X iff for any G open set xEG then there exist A Eẞ such
that x E ACG.
b\Let ẞ is a collection of open sets in X show that is base for a
topology on X iff for each xex the collection B, (BEB\xEB) is is a
nbhd base at x.
-
Q31 Choose only two:
al Let A be a subspace of a space X show that FCA is closed iff
F KOA, K is closed set in X.
الرياضيات
b\ Let X and Y be two topological space and f:X -…
Q1\ Let X be a topological space and let Int be the interior
operation defined on P(X) such that
1₁.Int(X) = X
12. Int (A) CA for each A = P(X)
13. Int (int (A) = Int (A) for each A = P(X)
14. Int (An B) = Int(A) n Int (B) for each A, B = P(X)
15. A is open iff Int (A) = A
Show that there exist a unique topology T on X.
Q2\ Let X be a topological space and suppose that a nbhd
base has been fixed at each x E X and A SCX show that A open
iff A contains a basic nbdh of each its point
Q3\ Let X be a topological space and and A CX show that A
closed set iff every limit point of A is in A.
A'S A
ACA
Q4\ If ẞ is a collection of open sets in X show that ẞ is a base
for a topology on X iff for each x E X then ẞx = {BE B|x E B}
is a nbhd base at x.
Q5\ If A subspace of a topological space X, if x Є A show
that V is nbhd of x in A iff V = Un A where U is nbdh of x in
X.
+
Theorem: Let be a function from a topological
space (X,T) on to a non-empty set y then
is a quotient map iff
vesy if f(B) is closed in X then & is
>Y. ie Bclosed in
bp
closed in the quotient topology induced by f
iff (B) is closed in x-
التاريخ
Acy
الموضوع :
Theorem:- IP & and I are topological space
and fix sy is continuous
او
function and either
open or closed then the topology Cony is the
quatient topology p
proof:
Theorem: Lety have the quotient topology
induced by map f of X onto y.
The-x:
then an arbirary map g:y 7 is continuous
7.
iff gof: x > z is
"g of continuous
Continuous function
f
Chapter A Solutions
EBK INTERMEDIATE ALGEBRA
Ch. A - 1. Write a fraction expression equivalent to with...Ch. A - Write a fraction expression equivalent to 34 with...Ch. A - Multiply by 1 to find three different fraction...Ch. A - Simplify. 1845Ch. A - Simplify.
5.
Ch. A - Simplify. 7227Ch. A - Simplify. 3256Ch. A - Simplify. 2754Ch. A - Simplify. 4812Ch. A - Multiply and simplify. 652512
Ch. A - Multiply and simplify. 385372Ch. A - Add and simplify. 45+35Ch. A - Add and simplify.
13.
Ch. A - Add and simplify.
14.
Ch. A - Add and simplify.
15.
Ch. A - Subtract and simplify.
16.
Ch. A - Subtract and simplify. 51229Ch. A - Find each reciprocal. 411Ch. A - Find each reciprocal. 157Ch. A - Find each reciprocal. 5Ch. A - Find each reciprocal. 13Ch. A - 22. Divide by multiplying by 1:
Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide by multiplying by the reciprocal of the...Ch. A - Divide and simplify.
27.
Ch. A - Divide and simplify.
28.
Ch. A - a Write an equivalent expression for each of the...Ch. A - a Write an equivalent expression for each of the...Ch. A - a Write an equivalent expression for each of the...Ch. A - a Write an equivalent expression for each of the...Ch. A - Write an equivalent expression with the given...Ch. A - Write an equivalent expression with the given...Ch. A - b Simplify. 1827Ch. A - b Simplify.
8.
Ch. A - b Simplify. 5614Ch. A - b Simplify. 4827Ch. A - b Simplify. 642Ch. A - b Simplify. 13104Ch. A - b Simplify. 567Ch. A - b Simplify. 13211Ch. A - b Simplify. 1976Ch. A - b Simplify. 1751Ch. A - b Simplify. 10020Ch. A - b Simplify. 15025Ch. A - b Simplify.
19.
Ch. A - b Simplify. 625325Ch. A - b Simplify.
21.
Ch. A - b Simplify. 48001600Ch. A - b Simplify.
23.
Ch. A - b Simplify.
24.
Ch. A - c Compute and simplify.
25.
Ch. A - c Compute and simplify. 151685Ch. A - c Compute and simplify.
27.
Ch. A - c Compute and simplify. 10111110Ch. A - c Compute and simplify.
29.
Ch. A - c Compute and simplify. 45+815Ch. A - c Compute and simplify. 310+815Ch. A - c Compute and simplify. 98+712Ch. A - c Compute and simplify. 5434Ch. A - c Compute and simplify.
34.
Ch. A - c Compute and simplify.
35.
Ch. A - c Compute and simplify.
36.
Ch. A - c Compute and simplify.
37.
Ch. A - c Compute and simplify.
38.
Ch. A - c Compute and simplify. 89415Ch. A - c Compute and simplify.
40.
Ch. A - c Compute and simplify. 1312395Ch. A - c Compute and simplify.
42.
Ch. A - c Compute and simplify. 10015Ch. A - c Compute and simplify. 7816Ch. A - c Compute and simplify. 3410Ch. A - c Compute and simplify.
46.
Ch. A - c Compute and simplify.
47.
Ch. A - c Compute and simplify. 147502
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