Let X be a set, and ✅ C P(X) a family with the properties: (1). Ø, X belong to A. (2). The intersection of any family of members of is also a member of A. (3). The finite union of members of belongs to A. Then = {CA | A € } is a topology, in which is the complete family of closed sets.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Prove:

Let X be a set, and A C P(X) a family with the properties:
(1). Ø, X belong to A.
(2). The intersection of any family of members of A is also a
member of A.
(3). The finite union of members of
belongs to A.
Then
= {CA | Ae} is a topology, in which is the complete
family of closed sets.
Transcribed Image Text:Let X be a set, and A C P(X) a family with the properties: (1). Ø, X belong to A. (2). The intersection of any family of members of A is also a member of A. (3). The finite union of members of belongs to A. Then = {CA | Ae} is a topology, in which is the complete family of closed sets.
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