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What axioms must be satisfied for a collection of subsets to be called a topology on a set?

There are three axioms that must be satisfied for a collection of subsets, t, of set B to be called a topology on B.1) Both B and the empty set, Ø, must be members of t.2) The intersection of any two members of t must also be a member of t.3) The union of any family of members of t must also be a member of t.If these axioms are met, the members of t are known as t-open or simply open, subsets of B.See related links.


Can you relate the number of elements of a set to its number of subsets?

If the set has "n" elements, then you can make 2n different subsets. The number of subsets will always be greater than the size of the set, both for finite and for infinite sets.


Does there exist a quadratic equation whose coefficients are irrational but both the roots are rational?

None, if the coefficients of the quadratic are in their lowest form.


Are integers and rational numbers related to real numbers?

Both are subsets of the real numbers.


How are Athens and Sparta the same?

Both Athens and Sparta had an Assembly, whose members were elected by the people


Is a set of rational number a sub set of irrational number?

No, they are disjoint sets. Both are subsets of the Real numbers.


What are regions in venn diagrams?

The universal set is represented by a rectangle. Subsets of this set are represented by closed curves (often circles). A ⊂ € Further subsets are represented by a closed curve within a larger closed curve. Q ⊂ P ⊂ € The intersection of two sets (A & B) is the set of elements that are members of both A & B and is usually shown as a shaded region. A ∩ B The union of two sets (A & B) is the set of all elements contained in A & B. A ∪ B.


Do both positive and negative integers exist?

Yes, both positive and negative integers exist.


Who is the leader of the minority party in the lower house responsible for informing party members and organizing resistance to programs submitted by the majority?

The leader of the minority party in the lower house responsible for informing members and organizing resistance to the majority is the whip. Whips exist in both houses and both the majority and minority parties to get party members on the same page.


How are rational numbers and integal numbers related to set of real numbers?

Both rational numbers and integers are subsets of the set of real numbers.


Both Barack Obama and John McCain are members of which legislative house?

They are both members of the Senate.


Does Damien exist?

If you are referring to Damien, the fictional character from the movie series 'The Omen,' no he does not exist. However, there is both a Saint Damien and a Saint Damian, both who do exist.