On some parallelism between complete regularity and zero-dimensionality |
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| Authors: | Oghenetega Ighedo Martin M Mugochi |
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| Institution: | 1. Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Pretoria, South Africaighedo@unisa.ac.za;3. Department of Mathematics, University of Namibia, P.O. Box 13301, Windhoek, Namibia. E-Mail mmugochi@unam.na |
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| Abstract: | We explore some parallelism between the categories CRFrm and 0DFrm of completely regular frames and zero-dimensional frames, respectively, with a view to establishing zero-dimensional analogues of C*-quotients. A lattice homomorphism between the cozero parts of two completely regular frames can be lifted to a frame homomorphism between the Stone-?ech compactifications of the frames involved 13]. Here we lift a lattice homomorphism ψ: BL → BM between the Boolean parts of two zero-dimensional frames to a frame homomorphism  | |
| Keywords: | Primary: 06D22 Secondary: 54C45 54D30 |
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