Determining continuity complex plane

Assignment Help Mathematics

Reference no: EM13127661

Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imaginary axes.

The 2 theorems are:

1). Theorem: Suppose f: X --> omega is continuous and X is compact; then f is uniformly continuous. ( of course we are talking about complex plane remember that)

2).Theorem: If A and B are non-empty disjoint sets in X with B closed and A compact then d(A,B) > 0.

Please I want a very detailed answer and justify every claim or statement in the solution. Please show where each theorem was used and why..I want to fully understand this problem. Thanks.

Polygon is a polygonal line..so Q is composed of lines which are parallel to either the x-axis or y-axis

Reference no: EM13127661

Questions Cloud

Find probability that the mean weight of loads is less : If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 47.6 tons. Assume that the variable is normally distributed.

What is the most popular functional currency : What is the most popular functional currency?

Problem related to bank reconciliation : A check drawn by a depositor for $180 in payment of a liability was recorded in the journal as $810? This item would be included on the bank reconciliation as?

Where is the piston located : A 1-ft-diameter cylinder is closed on one end and fitted with a moveable piston on the other. With 1 atm applied pressure, the piston is located 20 ft from the closed end

Determining continuity complex plane : Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imag..

What is the percentage price change of these bonds : Bond J is a 4 percent coupon bond. Bond S is a 11 percent coupon bond. Both bonds have eight years to maturity, make semiannual payments, and have a YTM of 7 percent. If interest rates suddenly rise by 4 percent, what is the percentage price chang..

Find standard deviation of number of hours worked per week : Suppose 12% of these workers work more than 48 hours. Based on this percentage, what is the standard deviation of number of hours worked per week for those workers.

Amount of unexpired insurance : Journalize the adjusting entry required at the end of the year assuming the amount of unexpired insurance related to future periods is 4,200.

Computer does not have to "understand" : What steps must the computer carry out? Think about the input (printed words), the output (spoken words), and the steps that must happen in between.

User Account

All Pages