Continuity

Topology of R: adhesion, interior, vicinity of a point,
Limits: quantified definition, uniqueness, operations, sequential characterization, limits and framing.
Continuity: definition, extension by continuity, continuity on a part, discontinuities of the first and second kind
Intermediate value theorem and its consequences for continuous functions on segments (thm of bijection, bounds reached on a segment, image of an interval, of a segment by a continuous function, homeomorphism theorem, injective + continuous => strictly monotone)...
Some usual limits for "simple" limit calculation (including comparative growths). Not too technical limits, integer function.