Understanding Open Covers

  • 12th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
Review Board Member
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
 , MBA
By Thames
T
Thames
Community Contributor
Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 15 | Updated: Jan 21, 2026
Please wait...
Question 1 / 16
🏆 Rank #-- ▾
Score 0/100

1) An open cover of a set is:

Explanation

An open cover is a family of open sets whose union contains the set.

Submit
Please wait...
About This Quiz
Understanding Open Covers - Quiz

Covers and subsets can feel abstract. In this quiz, you’ll get comfortable identifying open covers and their role in compactness. Take this quiz to build foundational intuition.

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) Which is an open cover of [0,1]?

Explanation

These two open intervals together cover [0,1].

Submit

3) Every finite set in ℝ is compact.

Explanation

Finite sets are always compact because any cover has a finite subcover.

Submit

4) Which of these is an open set in ℝ?

Explanation

Open intervals exclude endpoints.

Submit

5) Which is not an open cover of (0,1)?

Explanation

(−1,2) contains closed endpoints, not an open cover.

Submit

6) A finite subcover is:

Explanation

Compactness means every open cover has a finite subcover.

Submit

7) True/False: An open cover may consist of infinitely many sets.

Explanation

Covers can be infinite collections.

Submit

8) The union of sets in an open cover is:

Explanation

The union must contain the set fully.

Submit

9) Which of the following is an open cover of (0,1)?

Explanation

Together these intervals cover (0,1).

Submit

10) Open covers can overlap.

Explanation

Covers often overlap; disjointness is not required.

Submit

11) Compactness in ℝⁿ relates to:

Explanation

By Heine–Borel, compact = closed + bounded.

Submit

12) Which is compact in ℝ?

Explanation

[0,1] is both closed and bounded.

Submit

13) (0,1) is compact.

Explanation

Open intervals are not compact.

Submit

14) Which of these is not compact?

Explanation

(0,1) is open, hence not compact.

Submit

15) Compactness ensures:

Explanation

Definition of compactness.

Submit
×
Saved
Thank you for your feedback!
View My Results
Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
Cancel
  • All
    All (15)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
An open cover of a set is:
Which is an open cover of [0,1]?
Every finite set in ℝ is compact.
Which of these is an open set in ℝ?
Which is not an open cover of (0,1)?
A finite subcover is:
True/False: An open cover may consist of infinitely many sets.
The union of sets in an open cover is:
Which of the following is an open cover of (0,1)?
Open covers can overlap.
Compactness in ℝⁿ relates to:
Which is compact in ℝ?
(0,1) is compact.
Which of these is not compact?
Compactness ensures:
play-Mute sad happy unanswered_answer up-hover down-hover success oval cancel Check box square blue
Alert!