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Neither first countable nor Cech-complete spaces are maximal Tychonoff connected |
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| Authors: | D B Shakhmatov M G Tkacenko V V Tkachuk S Watson R G Wilson |
| Institution: | Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790, Japan ; Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacán y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México, D.F. ; Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacán y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México, D.F. ; Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3 ; Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacán y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México, D.F. |
| Abstract: | A connected Tychonoff space  is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on  . We show that if  is a connected Tychonoff space and  locally separable spaces, locally \v{C}ech-complete spaces, first countable spaces , then  is not maximal Tychonoff connected. This result is new even in the cases where  is compact or metrizable. |
| Keywords: | Connected space separable space \v{C}ech-complete space first countable space finer connected topology maximal connected topology |
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