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2 results for starlike-equivalence

Null, recursively starlike-equivalent decompositions shrink metric spaces.

problem Understanding the structure of metric spaces through recursive starlike-equivalence.
method Proving that any null, recursively starlike-equivalent decomposition of a compact metric space shrinks.
result The quotient map of a compact metric space under a null, recursively starlike-equivalent decomposition is a limit of homeomorphisms.

New theorem removes uniform finite upper bound for shrinkability of null decompositions.

problem Shrinkability of null decompositions with non-singleton elements.
method Defining squeezable and squashable subsets, proving their equivalence, and applying these definitions to null decompositions.
result Any null decomposition of a compact metric space whose non-singleton elements are recursively squeezable is shrinkable.