Some more examples of monotonically Lindelöf and not monotonically Lindelöf spaces |
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Authors: | Ronnie Levy |
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Institution: | Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA |
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Abstract: | A space is monotonically Lindelöf (mL) if one can assign to every open cover U a countable open refinement r(U) (still covering the space) so that r(U) refines r(V) whenever U refines V. Some examples of mL and non-mL spaces are considered. In particular, it is shown that the product of a mL space and the convergent sequence need not be mL, that some L-spaces are mL, and that Cp(X) is mL only for countable X. |
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Keywords: | 54D20 |
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