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Paratopological (topological) groups with certain networks

Chuan Liu — 2014

Commentationes Mathematicae Universitatis Carolinae

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, k -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...

A note on paratopological groups

Chuan Liu — 2006

Commentationes Mathematicae Universitatis Carolinae

In this paper, it is proved that a first-countable paratopological group has a regular G δ -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [, Topology Appl. (2006), 1917–1929]. If G is a symmetrizable paratopological group, then G is a developable space. We also discuss copies of S ω and of S 2 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]...

On weakly bisequential spaces

Chuan Liu — 2000

Commentationes Mathematicae Universitatis Carolinae

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.

Reconstruction algorithms for an inverse medium problem

Ji-Chuan Liu — 2018

Applications of Mathematics

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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