
Compact and Closed Sets in Topology

Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Hard

Thomas White
FREE Resource
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11 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main topic discussed in this video?
Probability Theory
Differential Equations
Open, Closed, and Compact Sets
Linear Algebra
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is an epsilon-neighbourhood?
A set of points with no relation to x
A single point x on the number line
An interval from (x - epsilon) to (x + epsilon)
A set of points exactly at distance epsilon from x
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a neighbourhood of a point x?
A set of points at a fixed distance from x
A single point x
A set of points with no relation to x
Any subset of real numbers containing an epsilon-neighbourhood of x
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is true about open sets?
They are always finite
They are neighbourhoods for all their points
They are not related to epsilon-neighbourhoods
They must contain all boundary points
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key characteristic of open sets?
They are always closed
They exclude all boundary points
They are always infinite
They include all boundary points
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is a closed set defined in terms of its complement?
Its complement is the empty set
Its complement is neither open nor closed
Its complement is an open set
Its complement is a closed set
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following sets is both open and closed?
The interval [0, 1]
The set of all integers
The empty set
The interval (0, 1)
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