Complete the definition of a metric space by filling in the three blonks: A metric space is a pair (s, d) where S is a set ond >[9L) di is a function such sheet - = (x₁y) = (y₁x) for all a d X, y es √ (X, Z) ≤ for all x y₁z € SA

Q: Let V be a real inner product space, and let u, v, w E V. If (u, v) = 1/2 and (v, w) = -2, what is…

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Q: Ex: Let d is a trivial metric o space ) show that every infir

A: We have given trivial metric space d on infinite set X. We have to show that every infinite subset…

Q: Let N R R be any norm on Rn. Show that N is a convex function (give all the details for the proof).

A: Given N :R^n→R be a norm on R^n.      To show : N is a convex.     Definition of norm :…

Q: let (x, m) be a measurable space. then ¥8:% [, o] are measural ble funetion, then ) I +9 is mea…

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Q: For example (X,d) metric space with d is a Euclidean metric. if set A = { = |neN} CX nEN CX and…

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Q: E. Let H be the set of all points (x, y) in R² such that x² + 3y² = 12. Show that H is a closed…

A: We have to find H is closed  subset bounded.

Q: Function f is defined by the equation above for all pairs (x,y) of real numbers such that f(x,y) is…

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Q: pls explain to me step by step. pls dont skip any steps. thanks

A: Proof:The metric defined on R is d (x, y) = |x – y|.In order to prove the real line is a metric…

Q: ) Give definition to the convex set of the space Rn. Also give a definition for when the function f…

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Q: W and V are linear spaces with dimension 2, the base of each of which is (e,, ez). If the linear…

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