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Problem 2.45. Can you define the basis generated by a subbasis?

Problem 2.45. Can you define the basis generated by a subbasis?

Advanced Engineering Mathematics
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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Solve 2.45 and 2.46

please don't copy from chegg, also attempt only when you know the right answer.

Definition 2.44. A set S is a subbasis for a topology on a set X provided US = X. The topology T on X generated by S is defined to be the collection of all unions of finite intersections of elements of S. Problem 2.45. Can you define the basis generated by a subbasis? Exercise 2.46. Show that: (1) The topology generated by a subbasis is a topology. (2) The sets in the subbasis are open sets in that topology.
Transcribed Image Text:Definition 2.44. A set S is a subbasis for a topology on a set X provided US = X. The topology T on X generated by S is defined to be the collection of all unions of finite intersections of elements of S. Problem 2.45. Can you define the basis generated by a subbasis? Exercise 2.46. Show that: (1) The topology generated by a subbasis is a topology. (2) The sets in the subbasis are open sets in that topology.
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