Abstract In this paper the application of homotopy equivalence transformation (HET) of topological space sets to the topological classification of states and defects in ordered media is discussed. Firstly, an argument is pres-ented about the idea that for simplifying and even working out the classification and constructing homotopy class sets into groups, it is crucial to utilize the HET. As the theoretical basis for doing this we sum up the relevant results in homotopy theory into a theorem, called the "invariance theorem for HET". Secondly, in order to favor the utilization of this theorem, several propositions on homotopy equivalence between space sets are given. Finally, the absolute and relative topological dassification of states and defects is systemtically studied. The main results obtained are embodied in eight theorems.
Received: 06 August 1992
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China.
Cite this article:
LI BO-ZANG (李伯臧), YAN FENG-LI (阎凤利) APPLYING THE HOMOTOPY EQUIVALENCE TRANSFORMATION OF TOPOLOGICAL SPACE SETS TO THE TOPOLOGICAL CLASSIFICATION OF STATES AND DEFECTS IN ORDERED MEDIA 1993 Acta Physica Sinica (Overseas Edition) 2 321
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
