New posts in semicontinuous-functions

Problem 3 chapter 12 Jost Postmodern analysis

Lower semicontinuous function as the limit of an increasing sequence of continuous functions

Upper semi continuous, lower semi continuous

Show that the supremum of a collection of lower semicontinuous function is lower semicontinuous

Show the iff statement of lower semicontinuous

Show that if $f^{-1}((\alpha, \infty))$ is open for any $\alpha \in \mathbb{R}$, then $f$ is lower-semicontinuous.

Subset of the preimage of a semicontinuous real function is Borel

Lower Semicontinuity Concepts

Show that every upper semi-continuous real function is measurable [duplicate]

Approximation of Semicontinuous Functions

Any lower semicontinuous function $f: X \to \mathbb{R}$ on a compact set $K \subseteq X$ attains a min on $K$.

To show that the supremum of any collection of lower semicontinuous functions is lower semicontinuous

What is the intuition for semi-continuous functions?