State whether the statement is true or false and justify your answer (f) The set B = {(r, y) € R² : z² + y² < 1} as a subset of R? with indiscrete metricis disconnected.(g) The empty set is path-connected.(h) The set of natural numbers as a subset of real numbers with the usual metricis compact.(i) Let f and g be uniformly continuous on a metric space X into R . Then theproduct f * g is uniformly continuous on X into R.

As per guidelines we have to attempt 1st three parts

Answered: (f) The set B = {(z, y) € R? : ² + y? <…

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 = {(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.