По The finite closed interval [a, b] is compact and no in both the Standard cofinito topology.

Q: Prove there exists a continuous surjection from the unit interval to the 2-sphere

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Q: (3) Let R² and R be endowed with their Euclidean metrics. (a) Show that projections p₁(x, y) = x and…

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Q: Let A, B and X be topological spaces. If A can not be embedded into B then A × X can not be embedded…

A: Let's first address the claim that S1 cannot be embedded into R. This claim is incorrect. The circle…

Q: Show the 3-dimensional ball B₁: ((..) ER³ | x² + y² +2² 0.

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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: Let (X, T) be a topological space and A C X. Prove that A =A.

A: PROOF :

Q: 3. Let (X, d) be metric space, prove that for any P1, P2, P3,..., Pn E X, we have d(p1, Pn) ≤d(p1,…

A: We prove the result by mathematical induction We know the triangle inequality of metric space If x,…

Q: If A, B are subsets of the topological space X show that Ext(AUB) = Ext(A)n Ext(B).

A: Given: A and B are subsets of the topological space X. To Prove: ExtA∪B=ExtA∩ExtB

Q: We note that ℤ2 which means ℤ*ℤ. Let d: ℤ2 *ℤ2→ℝ≥0 be the function that is given by…

A: The given in this question is a function d that takes two points (x0,y0) and (x1,y1) in the set of…