EDB — 2CV

12.1 Semi continuity[2CV]

Let \((X,𝜏)\) be a topological space. We define "liminf" and "limsup" generalizing the definition already presented in [20F]↺↻ when \(X={\mathbb {R}}\).

Note that \(f\) is lower semi continue if and only if \((-f)\) is upper semi continue: so in many subsequent exercises we will only see cases l.s.c. cases.

E2

[139]↺↻

E2

[13C]↺↻

E2

[13D]↺↻

E2

[13G]↺↻

E2

[13J]↺↻

E2

[13M]↺↻

E2

[13P]↺↻

E2

[13R]↺↻

E2

[13T]↺↻

E2

[13W]↺↻

E2

[13Y]↺↻

E2

[13Z]↺↻