The Categories of Boolean Lattices, Boolean Rings and BooleanSpaces
Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 245-252
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In Theorem 4 of [5] Stone stated that the theory of Boolean rings was"mathematically equivalent" to the theory of Boolean spaces without,however, properly defining the phrase "mathematically equivalent". It is themain purpose of this note to establish a precise reformulation of Theorem 4in [5]. This is accomplished by introducing special classes of maps betweenBoolean lattices, Boolean rings and Boolean spaces respectively, and showingthe categories arising in conjunction with these maps to be equivalent inthe sense of Grothendieck [2]. Thus the notion of equivalence of categorieswill replace the phrase "mathematically equivalent" in [5]. In addition thewell-known axiomatic characterization of meet and complementation of Booleanlattices with unit is discussed in analogous terms.
Doctor, Hoshang P. The Categories of Boolean Lattices, Boolean Rings and BooleanSpaces. Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 245-252. doi: 10.4153/CMB-1964-022-6
@article{10_4153_CMB_1964_022_6,
author = {Doctor, Hoshang P.},
title = {The {Categories} of {Boolean} {Lattices,} {Boolean} {Rings} and {BooleanSpaces}},
journal = {Canadian mathematical bulletin},
pages = {245--252},
year = {1964},
volume = {7},
number = {2},
doi = {10.4153/CMB-1964-022-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1964-022-6/}
}
TY - JOUR AU - Doctor, Hoshang P. TI - The Categories of Boolean Lattices, Boolean Rings and BooleanSpaces JO - Canadian mathematical bulletin PY - 1964 SP - 245 EP - 252 VL - 7 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1964-022-6/ DO - 10.4153/CMB-1964-022-6 ID - 10_4153_CMB_1964_022_6 ER -
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