(a) {(r, y) E R² : (x – 1)² + (y + 2)² < 1}. (b) {r €R: |r – 3| < 1}. (c) (0, 0) in R. (d) R\{0}.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Prove that each of the following sets is open in the appropriate vector space with usual
norm.
(a) {(x, y) E R² : (r – 1)? + (y + 2)² < 1}.
(b) {x € R : |x – 3| < 1}.
(c) (0, 00) in R.
(d) R\{0}.
Transcribed Image Text:2. Prove that each of the following sets is open in the appropriate vector space with usual norm. (a) {(x, y) E R² : (r – 1)? + (y + 2)² < 1}. (b) {x € R : |x – 3| < 1}. (c) (0, 00) in R. (d) R\{0}.
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