Consider the particular point topology, PPX, on a set X. Determine Int(A) and Cl(A) for sets A containing p and for sets not containing p.

Q: Show that Int(A) is an open set.

A:

Q: 6. How many mappings are there from A to B where A={1, 2, 3, 4} and B = {Low, Middle, High}. How…

A:

Q: Assume that A and B are nonempty, bounded above, and satisfy B CACR. Show that sup B < sup A.

A: Introduction: The supremum and infimum properties are the very important properties of any subset of…

Q: Let X be any set with the discrete topology. Show that X is normal.

A:

Q: Suppose that f is a function from A to B, where A and B are finite sets with |A| = |B|. Show that f…

A: Given that f is a function from A to B, where A and B are finite sets with A=B. We have to show that…

Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: Suppose that X and Y are topological spaces and f: X- Y. Show that f is continuous iff for each…

A: Definition: Let X and Y are topological spaces and f : X→Y be a function. We say that the function f…

Q: Let A be any set with the discrete topology. Show that A is normal.

A:

Q: We say that a set A is denumerable if there exists a bijective function f: N→ A. Suppose that A is a…

A:

Q: Exercise 2.16. Suppose that A and B are countably infinite sets. (A) Show that AUB is countably…

A: Suppose A and B are two countably infinite sets.  To prove that A∪B is also countably infinite.…

Q: Find an example of a nonempty set satisfying: 1. Closed, Dense in R 2. Open, Dense in R ~1. & 2.…

A:

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

A:

Q: Let A be a denumer able set. Prove that A has a denumer able subset B such that A - B is…

A: Let A =set of multiples of 4, B=set of multiples of 3. Both are denumerable. Intersection of A and B…

Q: Find an example of a topological space that is seperable and first countable but not second…

A:

Q: Indicate that  R and R2 may be covered by countably many open balls.

A: To show that ℝ and ℝ2 covered by countably many open balls.

Q: Using the Bisection method find the root of the polynomial f (x) = x³ – x – 2. use a = 1, b = 2

A:

Q: For any context-free grammar G, there exists a DFA DG such that L(Dg) = L(G).

A: True

Q: Find the value of z so that -8' 1 -4 is in the set M= span 12 2 2 Enter the value below:

A: Let's find.

Q: Show that the countable collection B = {(a,b) × (c, d)| a <b and c< d,

A:

Q: When is S \ T = T \ S for sets S, T? Give an example

A:

Q: What is the norm of a partition of a closed interval?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Need help with Discrete math, in specific Relations

A:

Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: Let C be a relation defined on the set of all geometric polygons, defined by any two polygons in the…

A: The given problem is from relation on sets. Here. Give that C be a relation defined on the set of…

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

A:

Q: Let a1, a2, ...,a, be real numbers that are all contained in the interval [-7/2, 7/2]. Use the…

A:

Q: Find a topology in which the point x = 5 is an open set.

A:

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: Let F be an event space. Show that F is closed under countable intersections.

A:

Q: Let A be a nonempty set and let f: A -> A be a function. Prove that if fof = iA, then f is…

A:

Q: Choose the correct option. The number of onto function from the set {1,2,….,11} to the set…

A: Let the set A be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and the set B be {1, 2, 3, 4, 5, 6, 7, 8, 9,…