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In this paper, by 1-sequence-covering mappings, the relations between metric spaces and spaces with (σ-) locally countable weak bases are established. These are answers to Alexandroff’s some problems.

In this paper, we study qualitative topological analysis of spaces of natural images locally. We apply the techniques of computational topology to the space of 3×3, 4×4, 5×5, 6×6 and 7×7 high-contrast patches. We show that in each case there is a subspace of the space of all high-contrast patches that is topologically equivalent to the Klein bottle and we… (More)

- MATEMATIQKI VESNIK, Shengxiang Xia
- 2007

In this paper, pseudo-sequence-covering π images and pseudo-sequence-covering, s, π images of locally separable metric spaces are discussed, their internal characterizations are given, which extends and improves the study of images of locally separable metric spaces.

- Shengxiang Xia, Gaoxiang Xia
- 2009

In this paper, we program a procedure using Maple's packages, with it we can realize mechanical proving of some theorems in elementary geometry.

- Shengxiang Xia, Wen Wang
- 2016

The method of computational homology is used to analyze natural image 8 × 8 and 9 × 9-patches locally. Our experimental results show that there exist subspaces of the spaces of 8× 8 and 9× 9-patches that are topologically equivalent to a circle and a Klein bottle respectively. These extend the results of the paper ”on the local behavior of spaces of natural… (More)

- Qingli Zhao, Shengxiang Xia, Zongcheng Li
- 2015 10th International Conference on P2P…
- 2015

With the rapid development of computing power and information processing ability, some efficient numerical methods are developed to deal with the complex problems. In this paper, efficient finite difference method is introduced to solve the nonlinear Laplacian problem, in which two variables can be approximated simultaneously. Calculation scheme is… (More)

- Shengxiang Xia, Wen Wang
- 2016

In this paper we use the nudged elastic band technique from computational chemistry to investigate sampled highdimensional data from a natural image database. We randomly sample 8×8 and 9×9 high-contrast patches of natural images and create a density estimator believed as a Morse function. By the Morse function we build one-dimensional cell complexes from… (More)

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