Let X be an infinite set equipped with the finite closed topology. A finite subset of X is a. closed b. орen c. clopen d. neither open nor closed

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: Use the Heine-Borel theorem to give an example of a set not compact in R with the usual topology…

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A: Let A=(1,2] and B=[1,2]

Q: Call a set A CR clopen if it is both open and closed. Prove that the only clopen sets are Ø and R.

A: A⊆R clopen if it is both open and closed.  We have to prove that the only clopen sets are ϕ and R

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Q: - If C is Convex set ond a GR, then XC is a Convex set

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Q: Let X be an infinite set equipped with the indiscrete topology T, then (X,T) is compact. * True…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

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

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Q: Let X be an infinite set, then any topology on X is also infinite. Select one: O True O False

A: Note: " Since you have asked multiple question. As per our guidelines we are supposed to solve only…

Q: X is not open, must it be closed? Either prove that every subset E that is not open must be closed,…

A: We will show it by giving example

Q: shows that there is no topology in X based on the family B = {{a, b}. {a, b, d}, {b, d, c}}

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Q: Show that any compact set in R is closed and bounded.

A: Proof

Q: A. Show that T is a topology in X and Show that B,(x) is open set with respect to t for all r > 0

A: This is a problem of Topology.

Q: Let X be an infinite set with the finite closed topology T={S subset of X; X-S is finite}. Then

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Q: A set L cR is convex if:

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Q: show that empty set, X is an element of S intersection T in topology

A: Here We have to show that empty set must be in S∩T where S and T are topology on set X.

Q: consider R with the usual topology then a subset A={1,0.5,..} is: empty or closed or open or none…

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Q: Let T be the finite closed topology and be also the discrete topology on a non empty set X. Then…

A: X is finite

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A: An infinite set equipped with discrete topology is not compact.

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Q: Let X be an infinite set with the countable closed topology T={S subset of X :X_S is countable}.…

A: We can show that X is countable. And by taking singleton we can solve the problem

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Q: let T be the finite closed topology on any set X.Every subset of (X,T) is connected true or false?

A: let T be the finite closed topology on any set X.Every subset of (X,T) is connected true or false?

Q: Let Cc R be a connected set and a , be R. Prove that [a , b] c C.

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Q: let E be a set that baunded. Prove that Inf E = Sup -E) where R, XE E y

A: To prove for a buonded set E inf(E) = -sup(-E) , where -E = {-x, x belongs to E} , we first prove…

Q: the collection of all close subsets of R is called the topology of R ylgn İhi

A: False

Q: Let T be the finite closed topology and be also the discrete topology on a non empty set X. Then* OX…

A: Gievn that Let T be the finite closed topology and be also the discrete topology on a non empty set…

Q: - A non-empty set E in R is connected if and only if it is an interval

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.