Show that the lower limit topology on R is strictly finer than the standard topology on R. That is: • Show that all sets that are open in the standard topology are open in the lower limit topology and • Also write an example of a set that is open in the lower limit topology that is not open in the standard topology. Justify why this example set is not open in the standard topology.

Show that the lower limit topology on R is strictly finer than the standard topology on R. That is: • Show that all sets that are open in the standard topology are open in the lower limit topology and • Also write an example of a set that is open in the lower limit topology that is not open in the standard topology. Justify why this example set is not open in the standard topology.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 29E: 29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there...

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