a) Let E be a nonempty subset of X. Prove that a is a cluster point of

Question:

a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E ∩ Br(a) \ (a) is nonempty.
b) Prove that every bounded infinite subset of R has at least one cluster point.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:16 AM

See More Questions

Let E be a nonempty subset of R and f be a real-valued function defined on E. Suppose that fn is a sequence of bounded functions on E which converges to f uniformly on E. Prove that uniformly on E as...
Let E be a nonempty subset of Rn. a) Show that a sequence xk E converges to some point a E if and only if for every set U, which is relatively open in E and contains a, there is an N N such that...
Let A be a nonempty subset of X that is partially ordered by . If A has a least upper bound, then it is unique. Similarly A has at most one greatest lower bound.
When would you suggest that an organization engage in workflow analysis?
Nova Electrics anticipated cash flow from operating activities of $6 million in 2011. It will need to spend $1.2 million on capital investments in order to remain competitive within the industry....
Here are facts for Haileys Collision Service for January. Assuming no investments or withdrawals, what is the ending balance in the owners capital account? Hailey Shusher, Capital Jan. 1 Jan. revenue...
1 3 Summarise at least one aspect of EU policy (or of an international trade agreement) which is of interest to you for your career
Keystone Computer Timeshare Company entered into the following transactions during May 2015. 1. Purchased computer terminals for $20,000 from Data Equipment on account. 2. Paid $3,000 cash for May...
Single-use cards, gave consumers a unique card number that was valid for one transaction only. Most of these card issuers found that people did not use them and withdrew them from the market. Select...
Contribution Margin Ratio a. Young Company budgets sales of $1,250,000, fixed costs of $50,600, and variable costs of $225,000. What is the contribution margin ratio for Young Company? 82 % b. If the...
Prove that a is a cluster point for some E X if and only if there is a sequence xn E \ {a} such that xn a as n .
Prove that if fn C[a,b], then fn f uniformly on [a, b] if and only if fn f in the metric of C[a, b] (see Example 10.6).
If you chose to ignore technology, explain how you will compensate for the loss of competitive advantage. If youre going to join one of the other two groups, explain why, and describe how you're...
The process of translating an idea into goods and services that create value or for which clients will pay is called
Let f be twice differentiable with f(0) = 6, f(1) = 8, and f'(1) = 7. Evaluate the following integral. [ = 0 0 xf" (x)dx
Although the Chen Company's milling machine is old, it is still in relatively good working order and would last for another 10 years. It is inefficient compared to modern standards, though, and so...
PART-3: OFFLINE QUESTIONS - Upload files using the submission link. 1. In 2020 Starbucks began a secret project to develop a competing product against the Keurig Single Serve coffee brewer. The...
As a leader, what are your highest values? o What's the contribution you want to make as a leader o What makes you distinct as a leader? o Drawing from StrengthsFinder 2.0 what are your strengths as...
Identify the likely effects on a cinema chain of uneven patterns of customer demand. Critically assess the methods that the cinema could use to overcome problems encountered.
Write a function that reads a Float24_t value: Float24_t float24_read(void) A legitimate float24 value string is of the form: "mantissabexponent" where the mantissa (m) and the exponent (e) may have...
Let Sn be the number of successes in n independent trials. Use the program BinomialProbabilities (Section 3.2) to compute, for given n, p, and j, the probability P (jnpq < Sn np < jnpq) . (a) Let p =...
Let X be a random variable taking on values a1, a2, . . . , pr with probabilities p1, p2, . . . , pr and with E(X) = μ. Define the spread of X as follows: This, like the standard deviation, is a...
Let X be a random variable with E(X) = μ and V (X) = σ2. Show that the function f(x) defined by
A family has a $117,443, 25-year mortgage at 5.4% compounded monthly. (A) Find the monthly payment and the total interest paid. (B) Suppose the family decides to add an extra $100 to its mortgage...
Comparing the actual and planned cost of a consulting engagement completed by an engineering firm such as Allied Engineering.
What is the NPV of a project that costs $34,000 today and is expected to generate annual cash inflows of $11,000 for the next 7 years, followed by a final inflow of $14,000 in year 8. Cost of capital...

a) Let E be a nonempty subset of X. Prove that a is a cluster point of

Question:

Step by Step Answer:

a Surely a set which has infinitely many points is nonempty Conversely if E B s a n a i...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions