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Weak extent, submetrizability and diagonal degrees | D. Basile
; A. Bella
; G. J. Ridderbos
; | Date: |
5 Dec 2011 | Abstract: | We show that if $X$ has a zero-set diagonal and $X^2$ has countable weak
extent, then $X$ is submetrizable. This generalizes earlier results from Martin
and Buzyakova. Furthermore we show that if $X$ has a regular
$G_delta$-diagonal and $X^2$ has countable weak extent, then $X$ condenses
onto a second countable Hausdorff space. We also prove several cardinality
bounds involving various types of diagonal degree. | Source: | arXiv, 1112.0883 | Services: | Forum | Review | PDF | Favorites |
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