in this paper we establish a characterization of abelian compact hausdorff semigroups with unique idempotent and ideal retraction property. we also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

Based on the characteristics of partial discharge (PD) defects in gas insulated switchgear (GIS), four typical single defects were designed for the present paper. PD three-dimensional (3D) patterns were constructed based on the ultra high frequency detection systems. The pulse-coupled neural networks (PCNN) and wavelet packet decomposition (WPD) method were used in PD feature extraction. The re...

The main result of this note is a parametrized version of the BorsukUlam theorem. Loosely speaking, it states that for a map X × S → S (with k < n), considered as a family of maps from S to S, the set of solutions to the Borsuk-Ulam problem (i.e. opposite points in S with the same value) depends continuously on X. We actually formuate this for correspondences. The “continuity” is measured by th...

We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the twopoint compactification of a locally compact ...

In this paper we introduce GF-compactifications, which are compactifications of GF-spaces (a new notion introduced by the authors). We study properties of this new kind of compactification and prove that every GF-compactification is of Wallman type. We also prove that every metrizable compactification of a metric space X is a GF-compactification and, as a corollary, that every metric compactifi...