Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Isolated Point, Interior Point, Exterior point, Boundary & Frontier Point
Isolated Point, Interior Point, Exterior point, Boundary & Frontier Point Video Lecture | Mathematics for Competitive Exams
FAQs on Isolated Point, Interior Point, Exterior point, Boundary & Frontier Point Video Lecture - Mathematics for Competitive Exams
| 1. What is an isolated point in mathematics? |  |
Ans. An isolated point in mathematics refers to a point that does not have any other point of a given set in its vicinity. In other words, it is a point that is not surrounded by any other points in the set.
| 2. How can we identify an interior point of a set? | |
Ans. To identify an interior point of a set, we need to check if there exists an open ball around the point, such that all the points within the ball are also part of the set. If such a ball can be found, then the point is considered an interior point of the set.
| 3. What is the difference between an interior point and an exterior point? | |
Ans. An interior point of a set is a point that is contained within the set, meaning it has an open ball around it that is entirely contained within the set. On the other hand, an exterior point is a point that is not part of the set and does not have any points from the set in its vicinity.
| 4. How can we determine the boundary of a set? | |
Ans. The boundary of a set consists of all the points that are neither interior points nor exterior points of the set. In other words, the boundary is the collection of points that are on the edge or boundary between the set and its complement. To determine the boundary, we need to find points that have both points from the set and its complement in their vicinity.
| 5. Can a point be both an interior point and a boundary point? | |
Ans. No, a point cannot be both an interior point and a boundary point simultaneously. An interior point is surrounded by points from the set, while a boundary point is on the edge between the set and its complement. Therefore, these two concepts are mutually exclusive.
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