A Selection Principle and Products in Topological Groups
We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/6/286 |
| Summary: | We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula> topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded group is an o-bounded group—Corollary 1. (2) In the generic extension by a finite support iteration of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℵ</mo><mn>1</mn></msub></semantics></math></inline-formula> Hechler reals the product of any o-bounded group with a ground model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℵ</mo><mn>0</mn></msub></semantics></math></inline-formula> bounded group is an o-bounded group—Theorem 11. (3) In the generic extension by a countable support iteration of Mathias reals the product of any o-bounded group with a ground model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℵ</mo><mn>0</mn></msub></semantics></math></inline-formula> bounded group is an o-bounded group—Theorem 12. |
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| ISSN: | 2075-1680 |