Abstract
We construct in ZFC a compactificationbℕ of integers such that the Boolean algebra Clopen(bℕ) is tree-like and every one-to-one continuous mapping as well as every continuous onto mapping frombℕ tobℕ is a homeomorphism, and every homeomorphism frombℕ onto itself is identity at all except finitely many points from ℕ.
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The research was supported by the grant GAUK 350.
The author owes sincere thanks to the referee, whose comments bridged many gaps in the first version of the present paper.
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Simon, P. An honest stiff tree-like algebra. Algebra Universalis 36, 450–456 (1996). https://doi.org/10.1007/BF01233915
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DOI: https://doi.org/10.1007/BF01233915