Unit · year 2
MU-201 · Real Analysis
Threads space · change6 theorems
Continuity, compactness and integration made rigorous on the real line.
Theorems in this unit
T-040
The intermediate value theorem
A continuous function takes every value between two of its values.
T-041
The Heine–Borel theorem
A subset of R^n is compact iff it is closed and bounded.
T-042
Uniform continuity on compact sets
Continuous on a compact set implies uniformly continuous.
T-043
The Riemann integrability criterion
A bounded function is integrable iff upper and lower sums can be made arbitrarily close.
T-044
Uniform limits of continuous functions
A uniform limit of continuous functions is continuous.
T-045
The Weierstrass M-test
A dominated series of functions converges uniformly.