4. Let Y + 0 and let A be a collection of subsets of Y satisfying the following two properties: (a) Y =U{A: A € A}; (b) for any {A, B} C A, we have AN BE A. If T = {DcY : 3{A;}ie1 C A such that D =U{A; : i e I}}, prove that T is a topol- ogy for Y and A is a basis for T.

4. Let Y + 0 and let A be a collection of subsets of Y satisfying the following two properties: (a) Y =U{A: A € A}; (b) for any {A, B} C A, we have AN BE A. If T = {DcY : 3{A;}ie1 C A such that D =U{A; : i e I}}, prove that T is a topol- ogy for Y and A is a basis for T.

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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Question

4. Let Y + 0 and let A be a collection of subsets of Y satisfying the following two
properties: (a) Y = U{A: A € A};
(b) for any {A, B} C A, we have An BE A.
If T = {D CY : 3{A;}ie1 C A such that D =U {A; : i e I}}, prove that T is a topol-
ogy for Y and A is a basis for T.

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