On real valued \(\omega\)-continuous functions (Q1737400)

Elementary properties of lower and upper $\omega$-continuous real functions defined on a topological space are investigated, analogous to the common topological case ($\omega$-closure is defined as the union of $A$ and all of its condensation points). In particular, definability in terms of counter-images, existence of extrema and properties of envelopes of arbitrary families of lower $\omega$-continuous functions are exhibited.