a) Let X = { a, b, c,d, e }, if B = {{a,b},{d,c}, {e, f}}forms a basis for X, find the topology generated by B. b) Let B = {(a, b) : a,b e Q} be the collection of open intervals in R with rational endpoints. Show that: (1) B is a basis for some topology on R. (2) The topology generated by B is the usual topology on R.

a) Let X = { a, b, c,d, e }, if B = {{a,b},{d,c}, {e, f}}forms a basis for X, find the topology generated by B. b) Let B = {(a, b) : a,b e Q} be the collection of open intervals in R with rational endpoints. Show that: (1) B is a basis for some topology on R. (2) The topology generated by B is the usual topology on R.

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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a) Let X = { a, b,c, d, e }, if B = {{a,b},{d,c},{e, f}}forms a basis for X,
find the topology generated by B.
{(a, b) : a,b E Q} be the collection of open intervals in R with rational endpoints. Show
b) Let B =
that: (1) B is a basis for some topology on R. (2) The topology generated by B is the usual
topology on R.

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