Justify the examples (c) and (d) in details (c) Let Ybe the set of non-zero real numbers with the subspace topologyof R. Then Y is disconnected since (-∞, 0) and (0, ∞) form a sep-aration.(d) Let Z = R²\R denote the plane minus the real axis, with the subspacetopology. Then Z is disconnected since the upper half plane U{(x,, x2) E R²: x2 > 0} and lower half plane V = {(x1, x2) E R²:X2 < 0} form a separation.%3D Definition: A topological space X is disconnected or separated if it is the unionof two disjoint, non-empty open sets. Such a pair A, B of subsets of X is called aseparation of X. A space X is connected provided that it is not disconnected. In otherwords, X is connected if there do not exist open subsets A and B of X such thatA + Ø, B+ Ø, ANB= Ø, AUB= X.%3DA subspace Y of X is connected provided that it is a connected space whenassigned the subspace topology. The terms connected set and connected subset aresometimes used to mean connected space and connected subspace, respectively.

Name: Justify the examples (c) and (d) in details (c) Let Ybe the set of non
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Justify the examples (c) and (d) in details (c) Let Ybe the set of non-zero real numbers with the subspace topologyof R. Then Y is disconnected since (-∞, 0) and (0, ∞) form a sep-aration.(d) Let Z = R²\R denote the plane minus the real axis, with th

Answered: Image /qna-images/answer/d6a93f97-9795-49ad-939f-34bc5a2e3e4a.jpg

Math

Advanced Math

(c) Let Y be the set of non-zero real numbers with the subspace topology of R. Then Y is disconnected since (–∞, 0) and (0, ∞0) form a sep- aration. (d) Let Z = R²\R denote the plane minus the real axis, with the subspace topology. Then Z is disconnected since the upper half plane U {(x1, x2) E R?: x, > 0} and lower half plane V = {(x,, x2) E R²: X2 < 0} form a separation. %3D

(c) Let Y be the set of non-zero real numbers with the subspace topology of R. Then Y is disconnected since (–∞, 0) and (0, ∞0) form a sep- aration. (d) Let Z = R²\R denote the plane minus the real axis, with the subspace topology. Then Z is disconnected since the upper half plane U {(x1, x2) E R?: x, > 0} and lower half plane V = {(x,, x2) E R²: X2 < 0} form a separation. %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: in details, what is the difference between direct and indirect relationships?

A: A direct relationship exists when the two variables (we'll call them x and y) shift in lockstep,…

Q: What is the correct answer ? I have to show work.

A: Given Information: Sample size (n) = 22 Mean (u) = 12 Standard deviation (s) = 5.4

Q: could you explain the steps you took to get there ?

Q: What does translation mean

A: Translation means moving every point of the figure by the same distance and in the same direction.

Q: How did you get those answers?

A: Since here we have two variables p and q, they can take values True (T) and False (F) each. So, the…

Q: The AM and GM for two observations are 5 and 4 respectively. Find the two observations.

Q: are the steps in order o

Q: Can you clarify the answer for the second step (a) ? It says that it's wrong.

A: as per the given data we can draw the following pond Let Q(t) be the amount of chemical (in kg) in…

Q: What are the two answers that I missed

Q: IF |A| = 2 AND |B| = 4, what is |A U B| + |A n B| ? PLEASE HELP

A: Given that |A| = 2 and |B| = 4

Q: I need help to do the exercises of the chart given for doing Excel and provide the steps as that…

A: Enter the data into the excel sheet as follows:

Q: What are verables for business math and can you show me an example

A: Variables are the quantity or value that can change over the context (experiment) in which it has…

Q: Write this as a set of equations: 4 2 -2 4 2 X2 10 3 -2 1 2 [2 0 3 -5

Q: How do you define mathematics?

Q: What is the answer? Can you be more detailed?

A: Fill these matrices from left sides....

Q: 12 (C) 18 ty percent use neither an iPhone no

A: The question number 26 and 27 are same. 26. The total number of students in a class is 60. nU=60.…

Q: 2x° 28 4y 28

Q: (AB) A-B→ ¬A

Q: (a) Construct a scatterplot of the weight (y) versus the height (x). Pass the ball: The NFL Scouting…

A: Given data: Height Weight 76 225 77 226 77 237 74 227 75 219 74 218 76 237 75…

Q: Could you explain part(b) as well?

A: Our objective is given below:

Q: What is i ? Explain.

A: In complex numbers, i represents the imaginary part. The value of i is -1. So, in case if we end…

Q: Need part d only to be answered!

A: note :As per the instruction we will only solve the part (d) of the question.To classify the…

Q: Which diagram shows the relationship between MMW students (S) and those that passed the exam (P)?…

Q: so what are the values of d and c?

Q: How do i do place the problem in the boxes

A: So we have to fit the multiplication in the table.

Q: Name 5. You have 350 yards of fencing to build a rectangular corral of length and width w. a. Write…

A: Given: The length of fence available is 350 yards. Length of rectangular coral is l and width is w.…

Q: 2. y -22+5

Q: Calculation: We take only P value. (b+f)P+(c+r)Q P = aQ+ (d+g)P+(e+s)Q ’ Take LCM…

A: The starting step is - P = aQ + (b+f)P+(c+r)Q(d+g)P+(e+s)Qtaking LCM we get,P =…

Q: Can you explain a bit more, I'm confused what the final answer is...

A: We’ve to find the probability that this sample average is less than 120 = P(X<120). Given that,…

Q: A survey found that women's heights are normally distributed with mean 62.3 in. and standard…

A: a. The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the…

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

100%

Justify the examples (c) and (d) in details

(c) Let Ybe the set of non-zero real numbers with the subspace topology
of R. Then Y is disconnected since (-∞, 0) and (0, ∞) form a sep-
aration.
(d) Let Z = R²\R denote the plane minus the real axis, with the subspace
topology. Then Z is disconnected since the upper half plane U
{(x,, x2) E R²: x2 > 0} and lower half plane V = {(x1, x2) E R²:
X2 < 0} form a separation.
%3D

Definition: A topological space X is disconnected or separated if it is the union
of two disjoint, non-empty open sets. Such a pair A, B of subsets of X is called a
separation of X. A space X is connected provided that it is not disconnected. In other
words, X is connected if there do not exist open subsets A and B of X such that
A + Ø, B+ Ø, ANB= Ø, AUB= X.
%3D
A subspace Y of X is connected provided that it is a connected space when
assigned the subspace topology. The terms connected set and connected subset are
sometimes used to mean connected space and connected subspace, respectively.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Propositional Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Yes, you did not say what a is and what b is. Their values
Can I get some help answer this?
The diagramm shows number of students who have TV, DVD, and Radio in different combinations. How many students have TV or DVD? (Assume that c = 2 )
Can you explain further the breakdown for part c please?
Plz solve in steps with explanation
course: discrete math
what about (ii) and (iii)???
12. Explain why the diagram displayed on the right cannot represent a real object.