In this paper, it is proved that a first-countable paratopological group has a regular -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [, Topology Appl. (2006), 1917–1929]. If is a symmetrizable paratopological group, then is a developable space. We also discuss copies of and of in paratopological groups and generalize some Nyikos [, Proc. Amer. Math. Soc. (1981), no. 4, 793–801] and Svetlichnyi [, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1989), 79–81]...
In this paper, we discuss certain
networks on paratopological (or
topological) groups and give positive
or negative answers to the questions
in [Lin2013]. We also prove that a
non-locally compact, -gentle
paratopological group is metrizable if
its remainder (in the Hausdorff
compactification) is
a Fréchet-Urysohn space with a
point-countable cs*-network, which
improves some theorems in
[Liu C., Metrizability of paratopological
semitopological groups,
Topology Appl. 159 (2012), 1415–1420],
[Liu...
Weakly bisequential spaces were introduced by A.V. Arhangel'skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.
In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability...
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