标题：On the topology of <mml:math alttext="$D$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi></mml:math>-metric spaces and generation of <mml:math alttext="$D$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi></mml:math>-metric spaces from metric spaces
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204311257
出版社：Hindawi Publishing Corporation
摘要：An example of a D-metric space is given, in which D-metric
convergence does not define a topology and in which a convergent
sequence can have infinitely many limits. Certain methods for
constructing D-metric spaces from a given metric space are
developed and are used in constructing (1) an example of a
D-metric space in which D-metric convergence defines a
topology which is T1 but not Hausdorff, and (2) an example of
a D-metric space in which D-metric convergence defines a
metrizable topology but the D-metric is not continuous even in
a single variable.
