Show that the closure of a connected space is connected.

Q: Find a star in the radial plane topology that does not contain any rationals.

A: The objective is to find the star in the radial plane topology which does not contain any rationals

Q: Exercise 3.55. Show that every wedge sum of Hausdorff spaces is Hausdorff.

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Q: Suppose (X, d) is a metric space and E a non-empty subset of X. Prove that E is disconnected if and…

A: Assume E is disconnected. Then there exist two open set U and V in E such that 1. U∩V=∅ 2. E=U∪V 3.…

Q: Suppose that Q : R" → R is a quadratic form attaining the minimum value on the set ||x|| = 1. %3D…

A: Given that                           Q : ℝn→ℝ is a quadratic form attaining the minimum value…

Q: Prove that a finite projective plane of order n has n2 + n + 1 points and n2 + n + 1 lines.

A: Let p be an ambitrany point, each point in it determinis a line together with P which Obviously…

Q: LBe M, N subsets of space W. Then span (MUN) = span (M) + span (N)“ %3D

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Q: Prove that continuous image of pathwise connected space is pathwise connected

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

Q: Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. biso (2) If…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Prove or give counter example an infinite product of discrete spaces may not be discrete

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Q: Determine the dimensions of the following spaces:    a) span ((1, 2, 3), (2, 4, 6), (3, 6, 9))…

A: In this question, we will find the dimensions of the spaces.

Q: Determine the dimension of the space spanned by the set

A: Given,               S=12-13, 1002, 28-48, 1111, 3306

Q: Suppose (X, d) is a metric space and E a non-empty subset of X. Prove that E is disconnected if and…

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