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Title: On Stone's representation theorem
Authors: Loo, Dong Lin
Keywords: Science::Mathematics
Issue Date: 2022
Publisher: Nanyang Technological University
Source: Loo, D. L. (2022). On Stone's representation theorem. Final Year Project (FYP), Nanyang Technological University, Singapore.
Project: MATH/21/067 
Abstract: Given a compact Hausdorff space X, we consider its regular open algebra, i.e. the Boolean algebra of all regular open subsets of X, RO(X). By Stone’s Representation Theorem, every Boolean algebra A is isomorphic to the clopen algebra of S(A), where S(A) denotes the Stone space of A. This thesis presents characterisations of the following three items: isomorphism of RO(X), Boolean embedding of RO(X) and quotient spaces of S(RO(X)). Analogues of the last two characterisations in the space of continuous real-valued functions on S(RO(X)) are presented. Some of our results are new and generalize previous known results.
Schools: School of Physical and Mathematical Sciences 
Fulltext Permission: restricted
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Student Reports (FYP/IA/PA/PI)

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