On distal and equicontinuous compact right topological groups
W. Ruppert has studied, and given examples of, compact left topological groups for which the left translation flow (λG,G) is equicontinuous. Recently, we considered an analogous distal condition that applies to the groups of dynamical type; for these the topological centre is dense, so the translati...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000529 |
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| author | Paul Milnes |
| author_facet | Paul Milnes |
| author_sort | Paul Milnes |
| collection | DOAJ |
| description | W. Ruppert has studied, and given examples of, compact left topological groups for which the left translation flow (λG,G) is equicontinuous. Recently, we considered an analogous distal condition that applies to the groups of dynamical type; for these the topological centre is dense, so the translation flow is equicontinuous only in the trivial case when G is topological. In the present paper, we continue this work, exhibiting new characterizations of equicontinuity and distality of (λG,G); we also discuss examples and study some related matters. |
| format | Article |
| id | doaj-art-b96209f73ef84a05af3671d66b1c62c4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b96209f73ef84a05af3671d66b1c62c42025-02-03T01:28:41ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117237938810.1155/S0161171294000529On distal and equicontinuous compact right topological groupsPaul Milnes0University of Western Ontario, Ontario, London N6A 5B7, CanadaW. Ruppert has studied, and given examples of, compact left topological groups for which the left translation flow (λG,G) is equicontinuous. Recently, we considered an analogous distal condition that applies to the groups of dynamical type; for these the topological centre is dense, so the translation flow is equicontinuous only in the trivial case when G is topological. In the present paper, we continue this work, exhibiting new characterizations of equicontinuity and distality of (λG,G); we also discuss examples and study some related matters.http://dx.doi.org/10.1155/S0161171294000529compact groupone-sided continuityequicontinuous flowdistal flow. |
| spellingShingle | Paul Milnes On distal and equicontinuous compact right topological groups International Journal of Mathematics and Mathematical Sciences compact group one-sided continuity equicontinuous flow distal flow. |
| title | On distal and equicontinuous compact right topological groups |
| title_full | On distal and equicontinuous compact right topological groups |
| title_fullStr | On distal and equicontinuous compact right topological groups |
| title_full_unstemmed | On distal and equicontinuous compact right topological groups |
| title_short | On distal and equicontinuous compact right topological groups |
| title_sort | on distal and equicontinuous compact right topological groups |
| topic | compact group one-sided continuity equicontinuous flow distal flow. |
| url | http://dx.doi.org/10.1155/S0161171294000529 |
| work_keys_str_mv | AT paulmilnes ondistalandequicontinuouscompactrighttopologicalgroups |