This post is currently awaiting moderation.
Question
In: Advanced Math
Is my proof that empty set is open and R is open correct?
Is that empty set is open and R is open correct? Give details Explaination.
Solutions
Expert Solution
Claim: The empty set is open.
Proof. Assume that the empty set is closed. Then, there must be one point such that any point in its ball is not inside of the empty set. However, the empty set has no point at all and therefore no such point and ball exists. This is a contradiction.
Claim: R is open.
Proof. Assume R is closed. Then its complement, the empty set, is open. But, we know that the empty set is closed. This is a contradiction.
Yes both are open.
Nipun Maity answered 2 years agoRelated Solutions
1) Show that if A is an open set in R and k ∈ R \...
1) Show that if A is an open set in R and k ∈ R \ {0}, then the
set kA = {ka | a ∈ A} is open.
let R be a ring; X a non-empty set and (F(X, R), +, *) the ring...
let R be a ring; X a non-empty set and (F(X, R), +, *) the ring
of the functions from X to R. Show directly the associativity of
the multiplication of F(X, R). Assume that R is unital and
commutative. show that F(X, R) is also unital and commutative.
( In R / R studio ) im not sure how to share my data set,...
( In R / R studio )
im not sure how to share my data set, but below is the
title of my data set and the 12 columns of my data
set.
Please answer as best you can wheather its pseudo code,
partial answers, or just a suggestion on how i can in to answer the
question. thanks
#----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
The dataset incovid_sd_20201001.RDatacontains several variables
related to infections of covid-19 for eachzip code in San Diego
County as of October...
Let X be a non-empty set and R⊆X × X be an equivalence relation. Prove that...
Let X be a non-empty set and R⊆X × X be an equivalence relation.
Prove that X / R is a partition of X.
Complete the proof for the claim that any open ball B(x0,r) in Euclidean space Rn is...
Complete the proof for the claim that any open ball
B(x0,r) in Euclidean space Rn is homeomorphic
to Rn.
proof is given below the theorem. Show that suggested map g is
in fact homeomorphism.
Theorem: Let X0, X1, and X2 be
topological spaces and let f: X0 -> X1 and
g : X1 -> X2 be continuous functions. Then
g∘f : X0 -> X2 is continuous.
proof : Suppose that V is open in X2. Since g is
continuous, g-1(V)...
Complete this formal proof of Ex(P(x)v~P(x)) from the empty set. NOTE: similar to the rule above...
Complete this formal proof of Ex(P(x)v~P(x)) from the empty set.
NOTE: similar to the rule above when instantiating quantifiers, if
you need a random name, always start at the beginning of the
alphabet. That is, use a first; only use b if necessary; etc.
An empty tin can with height of 30cm and a diameter of 15cm is open at...
An empty tin can with height of 30cm and a diameter of 15cm is
open at one end and closed at the other end. If the vertical can,
with open end down, be slowly immersed in water, how far the water
will rise inside the can when the closed end is 10 cm below the
water surface?
An empty tin can with height of 30cm and a diameter of 15cm is open at...
An empty tin can with height of 30cm and a diameter of 15cm is
open at one end and closed at the other end. If the vertical can,
with open end down, be slowly immersed in water, how far the water
will rise inside the can when the closed end is 10 cm below the
water surface?
I know this is easy, but when I'm solving for h, I'm
getting a negative value, means that the can will be filled...
Please correct my grammar's mistakes :) Please correct my grammar's mistakes, thanks! I chose to interview...
Please correct my grammar's mistakes :)
Please correct my grammar's mistakes, thanks!
I chose to interview Dinh, who is an active, assertive person
and a business major at ACC. Although he is not a math and science
major, he has already taken a lot of different science and math
classes. These classes include algebra, general chemistry one and
two, general physics one and two, and geometry, etc. Right now, he
is taking statistics and investments. Dinh told me that he...
1) a. Which of the following sets are the empty set? i. { x | x...
1)
a. Which of the following sets are the empty
set?
i. { x | x is a real number and x2 – 1 = 0 }
ii. { x | x is a real number and x2 + 1 = 0 }
iii. { x | x is a real number and x2 = -9 }
iv. { x | x is a real number and x = 2x + 1 }
b. Let A = {1, 2, 3,...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Instructions: Each of the following scenarios illustrates one of Freud’s defense mechanisms from the list below....
- What are the SHDN, LNA in opamp What are the TXCO coding algorithm for binary and...
- Need to program a maze traversal program using dynamic array and stacks. The problem is faced...
- what were some of Ida B Wells significant contributions to the civil rights movement?
- In 2007, there were many people in Sri Lanka who have an opinion that the government...
- Example #2: Write the following set of four linear equations with 4 unknowns x1, x2, x3,...
- "In the digital age, our personal and collective privacy is threatened like it never has been...
ADVERTISEMENT