The Heine-Borel Covering Theorem - Real Analysis | Lecture 8 скачать в хорошем качестве

The Heine-Borel Covering Theorem - Real Analysis | Lecture 8

In this theorem we discuss open sets, eventually moving toward stating and proving the celebrated Heine-Borel theorem. The fundamental example of an open set is an open interval, and we show that open sets can be thought of as being the union of (perhaps infinitely many) open intervals. Moreover, the Heine-Borel theorem shows us that an open cover of a closed finite interval has a finite subcover. These ideas will be utilized further in the following lecture when we use them to create an open and dense subset of the real numbers. This course is taught by Jason Bramburger.