Suppose metric space X is not path-wise connected then X is not connected. O True O False
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Q: 2) Show that the digital line topology on Z is not Hausdorff.
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A: Please check the answer in next step
Q: Suppose metric space X is not path-wise connected then X is not connected. O True O False
A: Question 9 Answer: as a path connected space of employees connected but converse is not true. So I…
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Q: Q: In usual topological space (R.Tu). answer the following: 1- Is [0,1] is compact set in R? Why?…
A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…
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Q: QUESTION 9 Suppose metric space X is not path-wise connected then X is not connected. True False
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Q: Hausdorff space.
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A: We use definition of connected and path connected sets. We use contradiction method.
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Q: The usuall metric space (Rd)isComplete ***
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A: Here, we introduce the notation Gr :=G∩[0, r) + 1-r ∪ G∩[r,1) - r for G⊂[0,1) and r∈R. Note that…
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Q: 7 The set M={xEN:x<÷} with the usual metric is connected.
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Q: (3) Let X be a connected, locally path connecte
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Q: For any metric space (X, d) and x EX, the singleton set (x) is closed. Select one: OTrue O False
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Q: Consider X = {a1, a2, ..., an} Can a topology of X with 3 open and one with 4 open be equivalent?
A: We have to verify the given statement.
Q: In any metric space, the only open and closed set at any time is the empty set and X only True False
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Q: 1. Prove that any ball (open or closed half open) in R³ is path connected. or
A: Definition: A topological space X is said to be a path connected space if given x, y∈X there exists…
Q: Prove that any ball (open or closed or half open) in R³ is path connected.
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Q: Suppose metric space X is not path-wise connected then X is not connected. True False
A: A space is said to be Path connected if we can fine a continuous function between any two points of…
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- 31. In Example 2.35, describe all possible configurations of lights that can be obtained if we start with all the lights off.Suppose metric space X is not path-wise connected then X is not connected. True FalseSuppose S be an open connected subset in arbitrary topological space X. Whether S is path connected or not?