In this paper we investigate completely homogeneous Ltopological spaces. The smallest completely homogeneous Ltopology on a set X containing an Lset f is called the principal completely homogeneous Ltopology generated by f . Here we also study the principal completely homogeneous Ltopological spaces generated by an Lset and characterize completely homogeneous Alexandroff discrete Ltopological s...

We study the behavior of certain spaces and their compactificability classes at infinity. Among other results we show that every noncompact, locally compact, second countable Hausdorff space X such that each neighborhood of infinity (in the Alexandroff compactification) is uncountable, has (X) = (R). We also prove some criteria for (non-) comparability of the studied classes of mutual compactif...

In this paper, we study fully non-linear elliptic equations in nondivergence form which can be degenerate or singular when “the gradient is small”. Typical examples are either equations involving the m-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of suc...

A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a σ-frame and to Alexandroff spaces.