Topology-6 (Examples of Open and Closed Sets)
In this lecture, some interesting examples of open and closed sets in topological spaces are discussed which reflects few beautiful pathologies associated with these two English words "open" and "closed".
Timestamps:
0:00 - Introduction
0:40 - Examples of sets which are both open and closed
9:15 - An example of set which is open but not closed
13:15 - An example of set which is closed but not open
16:30 - An example of set which is Neither closed nor open
20:36 - What can you say about arbitrary intersection of open sets ?
28:35 - An example in Euclidean plane which helps to understand and learn ways to write mathematical logics and the intuition in our mind.
42:54 - Conclusion