Show that the closure of a connected space is connected.

Q: Prove that any contraction between metric spaces has at most one fixed point

A: According to the given information, it is required to prove that any contraction between metric…

Q: Surface of a sphere is a two-dimensional Riemannian space. Compute the Chrtstoffel symbols.

A: Given: Surface of a sphere is a two-dimensional Riemannian space To find: Chrtstoffel symbols

Q: Ametric space (x,d) is complete if and only ifx has the cantor intersection property

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Q: Бxї Zet (x, г) бе space, then Co-countable тебя xis not Тз-брасе

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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: 1/ Let (X₁T) and (Y₁J.) be top spaces and fix-x be a surjective and continuousmap, then y is Compact…

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Q: a) Show that every closed subset of a compact space is compact but the converse need not to be true…

A: As per the guidelines I had given the proof of the first theorem. Kindly repost the another theorem…

Q: det (NT) is sPace Toflogecu! and T=0U{un}such that 7Show that (N, Cl is compact slase

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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: 4: state and prove L is a normed space ?

A: To prove that the space of bounded sequences, denoted as L^∞, is a normed space,we need to show that…

Q: A completely regular space is also T1-space 1 True 2 False

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Q: Question Show closed bale Y in Mebic space (X,d), Alsa ఎవక is set that ? then shaw is. complete d)is…

A: Given: Y is closed ball in metric space (X, d). To show:  1. Y is closed set in (X, d). 2. If (X, d)…

Q: Let (R,d) be diserete metric space then R is not compact . True or false.??

A: Let (R,d) be diserete metric space then R is not compact . True or false.??

Q: * Every Pre-Hilbert space is I - Continues Normed space -orthogonal Metric space inner Produced

A: Every pre-Hilbert Space is a complex vector space X together with an inner product (A complex inner…

Q: 1) Every convex set of a vector space X is affine set.

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Q: Other Math Yes a = [5 1], b = [1 4], c = [15 3], d = [8 13] Classify each of the following…

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Q: Show that finite dimensional inner product space is Hilbert space

A: We are to show that finite dimensional inner product space is Hilbert space.

Q: Don't use chat bot     Show that a compact Hausdorff is metrizable if it is locally metrizable.

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Q: Define metric space and define its four properties

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Q: (v) Prove that if the space (X,T) has the fixed-point property and (Y, T1) is a space homeomorphic…

A: Given: v) To prove the given statement as follows,

Q: 36) Prove that every product Space is inner metric Space- Discuss its Converse

A: Suppose that V is an inner product space over a field F. To prove that the V  is a metric space. To…

Q: If X is a Hausdorff topological space, is the quotient space X/∼ necessarily Hausdorff? Explain.

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Q: * Use the Grom Schmidt process for thi two_ dmensional space: 2 3. 4 2

A: Gram Schmidt process is given by: uk→=vk→−∑j=1k−1uj→⋅vk→|uj→|uj→   v1→=201, v2→=3-51, v3→=042,…

Q: Show that a set A in ℝ^ 2 is open in the Euclidean metric ⇔ it is open in the max metric.

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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: ctors - Z. S. Madhi

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Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

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: Provide an example to show that connectedness is not a hereditary property.

A: A property P1 is said to be hereditary: If any topological space X inherits the property P1 and all…

Q: Suppose X is a connected topological space with the property that every point x of X has a…

A: In this problem, we consider a connected topological space X with the property that every point in X…

Q: If S be a n-dimen Sional normed Space, then prove that its dual space is al so n- dimen Sional .

A: A normed space E is called a Banach space if it is complete, i.e., if every Cauchy sequence is…

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: Show that if a Banach space X is non-trivial, X + {0}, 3). then X' # {0}.

A: According to the given information, it is required to show that:

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: 1/ Let (X₁T) and (Y₁J.) be top spaces and fix-x be a surjective and continuousmap, then y is Compact…

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

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Q: / Let (X₁T) and (Y₁J) be top. Spaces and fix-x be a surjective and continuous map, then y is Compact…

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Q: Prove or disprove the following statement: A) Every T'3-space is T4-space?( explain your answer)

A: The statement "Every T3-space is a T4-space" is true. To understand why, let's first define the…

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: 9 Ex: Show that every finite space is compact space. Eulet die a trivial matrie on infinite catV(Y…

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Q: What is Sierpinski Space? Also give example

A: Sierpinski Space is  a topological space. Now to define a topological space we have to define a…

Q: Show that topologically completeness is weak hereditary property.

A: In this question, we have to show that completeness is a weak hereditary property.

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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