Form Classes

Statement:

\(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.)

Howard_Rubin_Number: 64

Parameter(s): This form does not depend on parameters

This form's transferability is: Transferable

This form's negation transferability is: Negation Transferable

Article Citations:
Howard-Yorke-1989: Definitions of finite
Levy-1958: The independence of various definitions of finiteness

Book references

Note connections:
Note 94 Relationships between the different definitions of finite
Note 57 Truss [1995] studies the various structures an amorphous set can carry.

The following forms are listed as conclusions of this form class in rfb1: 10, 64, 83, 127, 285, 390,

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Complete List of Equivalent Forms

Howard-Rubin Number Statement References
64 A

An amorphous power of a compact \(T_2\) space is compact.

Brunner [1984b]

64 B

Finite products of metric \(C\) spaces are \(C\). (A space is \(C\) if each open covering has an amorphous refinement.)

Brunner [1984b]

64 C

\(C\) spaces are compact. (A space is a \(C\) space if each open covering has an amorphous refinement.)

Brunner [1984b]

64 D

Metric \(C\) spaces are limited amorphous. (A space is \(C\) if every open covering has an amorphous refinement. A space is {\it limited amorphous} if each amorphous subset is relatively compact.)