🛈 This materials is useful for Unit 1 in CSIR-NET.
True or False: Let A and B be two connected subsets of a metric space. If B is a set such that A ⊆ B ⊆ C, then B is connected.
TRUE
Wrong. Taking counterexamples, let A = {1}, B = {1} U {2}, C = [1,2]. Clearly, the hypothesis is satisfied, but B is not connected.
FALSE
To prove, you need a proof. To disprove, you need a counterexample. Leave your proof below in comments!
Recommended Books for Real Analysis
Introduction to Real Analysis by Bartle and Sherbert (4e)
Principles of Mathematical Analysis by Rudin
Real Analysis by Kumaresan
Introduction to Topology and Modern Analysis by Simmons
Topology of Metric Spaces
Like this:
Like Loading...
Published by jessepfrancis
Christian. Artist. Mathematician. Programmer. Teacher.
Visit https://mathematicos.in/aboutjesse/ for my full profile.
View all posts by jessepfrancis