Define bounded set and an example of a set which is bounded below but not bounded above.

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: In the discrete topology on the set X, every set is open and it also follows that every set is…

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Q: Set A is bounded above if and only if set -A is bounded below.

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Q: Find an example of a nonempty set satisfying: • Open, every point is a limit point • Closed, every…

A: Just because a nonempty open set contains only limit points does not mean that the set contains all…

Q: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

Q: Give an example of a set in R ^ 2 with the usual topology that is not connected but has a connected…

A: Let's examine the  problem for path-connectedness example of a set in R2 with the usual topology…

Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: Define Open set ?

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Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: Give an example of a set w-limit that is a minimal set.

A: To give an example of a set w-limit that is a minimal set.  Given a collection of sets , a member…

Q: List all the subsets of the set A. Calculate the number of distinct subsets and proper suubsets for…

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Q: Prove a neighborhood is an open set

A: Recall that, a neighbourhood of a point is a set of points containing that point where one can move…

Q: The continuous image of a connected set is connected. That is, if X is connected and f: X→ Y is…

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Q: Define Closed sets ?

A: Closed sets are defined as a set which consists all of their limits points. It is also defined as…

Q: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

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Q: Choose any that is a subset of the set (Ø} {{Ø),0} {{1}}

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Q: Prove that (2,5) is an open set

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Q: A topological space is dis connected if and only if it contain non empty set which is both open and…

A: I give you two simple example with explanation

Q: Arbitrary unions of closed sets are closed.

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Q: The continuous image of a connected set is connected. That is, if X is connected and f : X–→ Y is…

A: We prove this via contradiction. We assume that f(X) is not connected then X is not connected. And…

Q: Show that any convex open set is simply connected.

A: The objective is to prove that any convex open set is simply connected. Simply connected is nothing…

Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: define sets.

A: A set is a collection of well defined objects.

Q: Give an example of a bounded set that has infinitely many isolated points

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

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Q: Use the definition of compact set to prove that the set [0,1] is compact

A: We know that a set E is compact if every open cover of E has a finite subcover. We suppose, that O…

Q: Determine if the union/intersection of two open sets is always open then determine if the…

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Q: subset

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Q: two example of open set in R, closed set in R, and the closure of that set

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Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: prove that empty set is a subset of every set

A: We have to prove that empty set is a subset of every set = ?

Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

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Q: Prove that derived set of a bounded set is also bounded.

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Q: Prove that a nonempty set is bounded if and only if it is contained in a bounded interval

A: A non empty set S is called bounded if it has both upper and lower bounds, In a certain sense a non…

Q: Set A is bounded below if and only if set -A is bounded above. True False

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Q: Show that any subset of bounded set is bounded

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Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

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Q: Give a set that is not closed under addition

A: In the question we have to give a set that is not closed under addition.

Q: Prove that the smallest member of a set, if exits, is the greatest lower bound of the set. Correct…

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Q: Prove that the greatest member of a set, if exits, is the least upper bound of the set,

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Q: ) Find an example of an infinite collection of closed sets whose union is not closed.

A: Any closed interval is closed in R. From that we created this example.

Q: Give an example of Partition set based on your real life situation and describe the disjoint subset…

A: Partition set: Partion sets of a set are non-empty subsets that consists of the elements of the set…

Q: undamental set

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Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: show vacuous proof of statement that "empty set is a subset of any set"

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Q: how that the union of a finite. number of bounded sets is bounded

A: A statement is given as, 'the union of a finite number of bounded sets is bounded. The objective is…

Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: Let X be infinite set and x0 ∈ X. Consider the topology τ = {G ⊆ X : x0 ∈ G or G = ∅} on X. Is (X, τ…

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Q: Give example closed set and bounded set is compact

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Q: Give example for following 1/ set is not compact

A: Compact set:- A set S⊆R is called compact “if every sequence in S has a subsequence that converges…