Baire Category Theorem

We explain the need for the concepts underlying the result and give two formulations for the theorem which are the ONLY way they are needed in applications (to the best of my knowledge). We avoid terms such as "category", "meager sets" and "Baire space" which obfuscate the real meaning of the theorem. Please leave your likes and comments below. Timestamp provided by Garima Khetawat. 00:00- Introduction 03:05- Motivation 04:47- Dense sets in a metric space 05:32- What does the theorem say and what are its uses? 07:06- The complement of an open and dense set is a closed set with an empty interior 09:10- Interior of a set 09:55- The complement of a closed set with an empty interior is an open dense set 12:44- Nowhere dense sets 14:11- Example of a nowhere dense set and an equivalent definition 20:18- Statement of the theorem 24:57- Equivalence of the two statements 26:37- Examining the first statement 30:40- Constructing the proof 46:19- Understanding the need to modify the proof 52:23- Some examples illustrating how to use the theorem