A Proof And An Extension Of A Theorem Of G. Birkoff
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Let X be a space. A space Y is called an extension of X if Y contains X as a dense subspace. For an extension Y of X the subspace Y∖X of Y is called the remainder of Y. Two extensions of X are said to be equivalent if there is a homeomorphism between them which fixes X pointwise. For two (equivalence classes of) extensions Y and Y' of X let Y ≤ Y' if there is a continuous mapping of Y' into Y which fixes X pointwise. Let 𝓟 be a topological property. An extension Y of X is called a 𝓟-extension...
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CONTENTSIntroduction....................................................................................... 5§ 1. On submeasures.................................................................... 6§ 2. Extension of submeasures................................................... 21§ 3. Extension of subcontents....................................................... 27References....................................................................................... 35
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