When one has the law of the excluded middle, then a subquotient X of Y is either the empty set or there is an onto function Y \ to X.
2.
If I do not misunderstand it means that for every compact space X there is a continuous onto function with domain the Cantor set and range X . But won't the cardinality of X be at most the continuum as if f is an onto function from A to B then | B | < = | A |?
3.
If I do not misunderstand it means that for every compact space X there is a continuous onto function with domain the Cantor set and range X . But won't the cardinality of X be at most the continuum as if f is an onto function from A to B then | B | < = | A |?
4.
To handle this, property-preserving isomorphisms ( 1-1 and onto functions between the objects of two worlds, whereby an object in one world has a property if and only if the object which that function takes you to in the other world does ) are used, and once this is done, several varieties of global supervenience can be defined.
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