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Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces |
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| Authors: | G Gruenhage V V Tkachuk R G Wilson |
| Institution: | a Department of Mathematics, Auburn University, Auburn, AL 36849, USA b Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa A.P. 55-532, C.P. 09340, México, DF, Mexico |
| Abstract: | We prove that any metrizable non-compact space has a weaker metrizable nowhere locally compact topology. As a consequence, any metrizable non-compact space has a weaker Hausdorff connected topology. The same is established for any Hausdorff space X with a σ-locally finite base whose weight w(X) is a successor cardinal. |
| Keywords: | Metrizable space Nowhere locally compact space Connected space Condensation |
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