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Monroe Eskew
Monroe Eskew
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I'm not sure if this is research level, so feel free to vote to migrate.

Suppose we have a complete boolean algebra $A$, with a dense, $\sigma$-complete subalgebra $B$, and a $\sigma$-complete homomorphism $h : B \to C$, where $C$ is complete. Does $h$ have a $\sigma$-complete extension $h' : A \to C$?

EDIT: I forgot to say that I'm interested in the case that $A$ is atomless.

I'm not sure if this is research level, so feel free to vote to migrate.

Suppose we have a complete boolean algebra $A$, with a dense, $\sigma$-complete subalgebra $B$, and a $\sigma$-complete homomorphism $h : B \to C$, where $C$ is complete. Does $h$ have a $\sigma$-complete extension $h' : A \to C$?

I'm not sure if this is research level, so feel free to vote to migrate.

Suppose we have a complete boolean algebra $A$, with a dense, $\sigma$-complete subalgebra $B$, and a $\sigma$-complete homomorphism $h : B \to C$, where $C$ is complete. Does $h$ have a $\sigma$-complete extension $h' : A \to C$?

EDIT: I forgot to say that I'm interested in the case that $A$ is atomless.

Source Link
Monroe Eskew
Monroe Eskew
  • 18.6k
  • 5
  • 53
  • 114

extending $\sigma$-complete boolean homomorphism

I'm not sure if this is research level, so feel free to vote to migrate.

Suppose we have a complete boolean algebra $A$, with a dense, $\sigma$-complete subalgebra $B$, and a $\sigma$-complete homomorphism $h : B \to C$, where $C$ is complete. Does $h$ have a $\sigma$-complete extension $h' : A \to C$?