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(f) The set B = {(z, y) € R? : ² + y? < 1} as a subset of R? with indiscrete metric is disconnected. (g) The empty set is path-connected. (h) The set of natural numbers as a subset of real numbers with the usual metric is compact.

(f) The set B = {(z, y) € R? : ² + y? < 1} as a subset of R? with indiscrete metric is disconnected. (g) The empty set is path-connected. (h) The set of natural numbers as a subset of real numbers with the usual metric is compact.

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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(f) The set B = {(r, y) € R² : z² + y² < 1} as a subset of R? with indiscrete metric is disconnected. (g) The empty set is path-connected. (h) The set of natural numbers as a subset of real numbers with the usual metric is compact. (i) Let f and g be uniformly continuous on a metric space X into R . Then the product f * g is uniformly continuous on X into R.
Transcribed Image Text:(f) The set B = {(r, y) € R² : z² + y² < 1} as a subset of R? with indiscrete metric is disconnected. (g) The empty set is path-connected. (h) The set of natural numbers as a subset of real numbers with the usual metric is compact. (i) Let f and g be uniformly continuous on a metric space X into R . Then the product f * g is uniformly continuous on X into R.
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