Limits of functions and topology of the real line
- Infinity as the value of the limit:
.
- Functions of real variable: the domain, range etc (recall). Examples: polynomial and rational functions,
. Compositions:
.
- Limit of a function: one-sided, two-sided. Continuity points.
- Sequential limit vs. “standard” limit: equivalence theorem.
- Open and closed subsets on the real line. סביבות וסגור
- Images and preimages. Some algebra of sets:
, the same with
. Warning:
. Operations on infinitely many sets (unions, intersections).
- Local and non-local properties of functions.
- Continuity via open/closed sets.
- Compactness and its implications.
Advertisements
Leave a Reply