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• W2007202237 abstract "In this note, we introduce concepts of JSM -spaces and JADM -spaces following a general idea of Arhangel'skii and Shumrani. Let X be a topological space. Denote F S ( X ) = { S ∪ { x S } : S is a convergent sequence of X which converges to the point x S } . A subspace Y of X is called almost discrete if Y has at most one non-isolated point. Denote F AD ( X ) = { Y : Y is an almost discrete subspace of X } . A space X is called a JSM-space ( JADM-space ) if there is a metric d on the set X such that d metrizes all subspaces of X which belong to F S ( X ) ( F AD ( X ) ). We get some conclusions on JSM -spaces and JADM -spaces. A space X is said to be weak Fréchet if for any σ -closed discrete subspace B of X with x ∈ B ¯ there is a sequence { x n : n ∈ N } ⊂ B which converges to x . We show that if X is a Hausdorff weak Fréchet compactly metrizable strong Σ ⁎ -space then X has a σ -locally finite network." @default.
• W2007202237 created "2016-06-24" @default.
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• W2007202237 creator A5086236273 @default.
• W2007202237 date "2015-06-01" @default.
• W2007202237 modified "2023-09-24" @default.
• W2007202237 title "A note on joint metrizability of spaces on families of subspaces" @default.
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• W2007202237 doi "https://doi.org/10.1016/j.topol.2015.03.002" @default.
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