This thesis is concerned With showing the relations among Boolean lattices, Boolean rings and Boolean spaces, It establishes that the categories of Boolean lattices and proper Boolean lattice homomorphisms, Boolean spaces and proper continuous maps, Boolean rings and proper ring homomorphisms are equivalent to each other, In the final chapter the notion of a Boolean semi-group is used to obtain an alternate characterization of a Boolean lattice. / Thesis / Master of Science (MS)

<p> In this thesis we introduce the concept of a dense extension of a partially ordered set and study some of the properties of the resulting class of extensions. In particular we study the dense distributive extensions, dense Boolean extensions and dense meet continuous extensions of distributive, Boolean and meet continuous lattices respectively.</p> / Thesis / Doctor of Philosophy (PhD)