## Abstract

A mapping between projections of C* -algebras preserving the orthogonality, is called an orthoisomorphism. We define the order-isomorphism mapping on C* -algebras, and using Dye's result, we prove in the case of commutative unital C* -algebras that the concepts; order-isomorphism and the orthoisomorphism coincide. Also, we define the equipotence relation on the projections of C(X); indeed, new concepts of finiteness are introduced. The classes of projections are represented by constructing a special diagram, we study the relation between the diagram and the topological space X. We prove that an order-isomorphism, which preserves the equipotence of projections, induces a diagram-isomorphism; also if two diagrams are isomorphic, then the C* -algebras are isomorphic.

Original language | English |
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Pages (from-to) | 523-536 |

Number of pages | 14 |

Journal | Turkish Journal of Mathematics |

Volume | 34 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2010 |

## Keywords

- Clopen subsets
- Commutative C* -algebras
- Infinite projections
- Projections order-isomorphism

## ASJC Scopus subject areas

- General Mathematics