ABSTRACT
This chapter contains a detailed investigation of the Stone-Cech compactification. The Stone-Cech compactification of a denumerable discrete space has cardinality while the space in which Tychonov embeds such a space has cardinality. In the late 1930’s and early 1940’s there are many references to “(bi) compactifications of Cech and Wallman.” Hewitt’s paper refers at least twice to the theorems of “Stone and Cech” and Dieudonne’s review of Hewitt’s paper refers to “la compactification bien connue de Stone-Cech.” As a concluding comment on this work of Stone, the authors refer to some comments of Alexandroff in the introduction to the 1971 edition of the Memoires: The work of M. Stone introduced to topology a new method – the method of Boolean algebra, the possibilities of which still have not been exhausted and only at the present time are beginning to be evaluated according to their merit.
