The Wallman Spaces and Compactifications

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If X is a topological space and Y is a ring of closed sets, then a necessary and sufficient condition for the Wallman space W(X,F) to be a compactification of X is that X be T1 andYF separating. A necessary and sufficient condition for a Wallman compactification to be Hausdoff is that F be a normal base. As a result, not all T, compactifications can be of Wallman type. One point and finite Hausdorff compactifications are of Wallman type.

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iii, 30 leaves

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Liu, Wei-kong December 1976.

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  • Liu, Wei-kong

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If X is a topological space and Y is a ring of closed sets, then a necessary and sufficient condition for the Wallman space W(X,F) to be a compactification of X is that X be T1 andYF separating. A necessary and sufficient condition for a Wallman compactification to be Hausdoff is that F be a normal base. As a result, not all T, compactifications can be of Wallman type. One point and finite Hausdorff compactifications are of Wallman type.

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iii, 30 leaves

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  • December 1976

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  • May 10, 2015, 6:16 a.m.

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  • June 23, 2016, 3:22 p.m.

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Liu, Wei-kong. The Wallman Spaces and Compactifications, thesis, December 1976; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc504392/: accessed October 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .