7. Let a, b ER, with a < b. Prove that each discrete subspace of R and each of the spaces [a, b]. (a, b). [a,b). (a,b]. (-∞, a). (-∞, a]. (a, ∞), [a, ∞), and {a}, with the topology induced as a subspace of R, is a Polish Space.
7. Let a, b ER, with a < b. Prove that each discrete subspace of R and each of the spaces [a, b]. (a, b). [a,b). (a,b]. (-∞, a). (-∞, a]. (a, ∞), [a, ∞), and {a}, with the topology induced as a subspace of R, is a Polish Space.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![CHAPTER 6. METRIC SPACES
7. Let a, b E R, with a < b. Prove that each discrete subspace of R and each of
the spaces [a, b]. (a, b). [a,b). (a,b], (-∞, a). (-∞, a], (a, oo), [a, ∞o), and {a},
with the topology induced as a subspace of R, is a Polish Space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50a8247f-f337-426c-a5da-8e3afbe0d0cc%2F7de18ddb-f680-4509-b29a-97c4065a1f55%2F2cwxb7_processed.png&w=3840&q=75)
Transcribed Image Text:CHAPTER 6. METRIC SPACES
7. Let a, b E R, with a < b. Prove that each discrete subspace of R and each of
the spaces [a, b]. (a, b). [a,b). (a,b], (-∞, a). (-∞, a], (a, oo), [a, ∞o), and {a},
with the topology induced as a subspace of R, is a Polish Space.
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