Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.Comment: With the participation of the new coauthor - Jimmie Lawson - the manuscript has been substantially revised and expanded. Accordingly, we have also changed the manuscript titl

Environmental resources of selected areas of Hawaii: Cultural environment and aesthetic resources

This report has been prepared to make available and archive the background scientific data and related information collected on the cultural environment and aesthetic resources during the preparation of the environmental impact statement (EIS) for Phases 3 and 4 of the Hawaii Geothermal Project (HGP) as defined by the state of Hawaii in its April 1989 proposal to Congress. The cultural environment in the Geothermal Resource Zone (GRZ) and associated study area consists of Native Hawaiian cultural and religious practices and both Native Hawaiian and non-Native Hawaiian cultural resources. This report consists of three sections: (1) a description of Native Hawaiian cultural and religious rights, practices, and values; (2) a description of historic, prehistoric, and traditional Native Hawaiian sites; and (3) a description of other (non-native) sites that could be affected by development in the study area. Within each section, the level of descriptive detail varies according to the information currently available. The description of the cultural environment is most specific in its coverage of the Geothermal Resource Subzones in the Puna District of the island of Hawaii and the study area of South Maui. Ethnographic and archaeological reports by Cultural Advocacy Network Developing Options and International Archaeological Research Institute, Inc., respectively, supplement the descriptions of these two areas with new information collected specifically for this study. Less detailed descriptions of additional study areas on Oahu, Maui, Molokai, and the island of Hawaii are based on existing archaeological surveys