on R.Question 3. Let r, and r, be two topologies on X such that 7,sr,.Construct a space on which a ,-limit point is not a r,-limit point of asubset A of X.Question 4. Let 8 and 8, be bases for topologies r, and r, respectively,on a non-empty set X. Suppose that each Be is the union of membersof 8. Show that r, is coarser than 7.

According to our guideline we can answer only first question only or three subparts and rest can be…

Answered: on R. Question 3. Let r, and be two…

on R. Question 3. Let r, and be two topologies on X such that Sr,. Construct a space on which a -limit point is not a r-limit point of a subset A of X.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

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A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because O 1-00,0] is homeomorphic to [0,+[ O Ris homeomorphic to ]0, +[ R is homeomorphic to ]0,1[ [0,1] is not homeomorphic to ]0,1[
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Number 2 HELP ME ASAP
Please answer the second question f(x,y,z)