Let X = R with the usual metric given by d(x, y) = Ix yl: Let A = [-2,0] U [3,4] € X endowed with the subspace metric: Which one of the following is not an open ball in A? Select one: a. [-2,-1) b. (-1, 0] U [3,4] c [-2, 0] d.(-1,0] U [3,3.5]
Added by Eva B.
Close
Step 1
Since A is a subset of X, we can use the same formula for the distance as in X, but only consider points in A. So, for any x, y ∈ A, we have: dA(x, y) = d(x, y) = |x - y| Show more…
Show all steps
Your feedback will help us improve your experience
Leigh Anne Emberg and 78 other Geometry educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
3.5. Let Y = (0, 5] have the subspace topology inherited from R with the lower limit topology. Which of the following subsets of Y are open, and which are closed, in Y in this topology? (a) (0,1) (b) (0,1] (c) {1} (d) (0,5] (e) (1,2) (f) [1,2) (g) (1,2] (h) [1,2] (i) (4,5] (j) [4,5]
Sri K.
Recommended Textbooks
Geometry A Common Core Curriculum
Geometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD