\(\varepsilon\)-spaces (Q1912622)

The notion of an \(\varepsilon\)-space is introduced as follows. A Tikhonov space \(X\) is called an \(\varepsilon\)-space if each Baire set \(E\) of \(\beta X\) disjoint from \(X\) is a subset of a countable union \(C\) of zero-sets of \(\beta X\) such that \(C\cap X= \emptyset\). Properties of \(\varepsilon\)-spaces are investigated. Consideration of \(\varepsilon\)-spaces is motivated by the observation that \(X\) is an \(\varepsilon\)-space iff the epicomplete epireflection of \(C(X)\) within a certain category of \(\ell\)-groups is just the \(\ell\)-group of Baire functions on \(X\).