1. Research on S- closed space and semi-topological space in general topology. In 1976, Thompson introduced the concept of S- closed space and discussed its properties. Wang Guojun found that Thompson's basic definition was very complicated, and the characteristic theorem about S- closed space was inconvenient to apply. The reasoning of some theorems is not simple enough, and the depth and breadth of some conclusions are limited. In addition, some results have been proved to be wrong. Therefore, he gave a simple definition of S- closed space, established a characteristic theorem which is convenient for application, and obtained some new properties of S- closed space. These results were published in the Journal of Mathematics of 198 1. Regarding the absolute closure of S- closed spaces, Wang also made in-depth research, and these results were published in Science Bulletin, 1982. Another major achievement of Wang Guojun in the field of general topology is the theory of semi-topological space. In 1977, he introduced two concepts of semi-topological space, and established the theories of open set, closed set, kernel, package, pseudo-package, penetration, net, continuous mapping, homeomorphism, product space and neighborhood compactness on semi-topological space. Two important applications of semi-topological space theory are given: one is to unify the concepts of weak continuous mapping, semi-continuous mapping, two almost continuous mapping and indefinite mapping; Secondly, the concepts of Hausdorff- closed space, Urysohn- closed space, complete Hausdorff- closed space, S- closed space and nearly compact space are unified. These results were published in Journal of Shaanxi Normal University in the form of 1977 and 1978. Later, many scholars did a lot of work on this basis. Dr. Chen, a student, introduced the concept of S-system in 1995 on the background of Wang's semi-topological space theory, and established the Stone duality theorem of L- fields on stable maps by using S-system.
2. Research on fuzzy topology theory. In 1965, American cybernetics experts L, A and professors put forward the theory of fuzzy sets, and in 1968, C, L and often introduced the concept of fuzzy topological space. Since then, C, L, Chang, C, K, Wong, B, Hutton, M.A.Erceg have appeared one after another. On the one hand, their research transplanted many contents of general topology into fuzzy topology, on the other hand, they also encountered many difficulties. The main reason is that they have not found the membership relationship between ideal fuzzy points and fuzzy sets. 1977, China mathematicians Pu Baoming and Liu Yingming introduced the concept of "heavy domain" and established a complete Moore-Smith sword-collecting theory. In 1979, Wang Guojun introduced the concept of far field, which was obtained by transforming and abstracting the concept of neighborhood in point set topology and the concept of heavy field in fuzzy topology. It is suitable for the study of L- fuzzy topology and topological molecular lattice theory. On the basis of domain method, Wang has made a series of research achievements in fuzzy topology research, one of which is good compactness theory. In clear topology, compactness has been deeply studied, but in fuzzy topology, the situation is more complicated. Although C, L and Chang gave the concept of fuzzy compactness when introducing fuzzy topological space, this compactness is simply obtained by imitating the concept of compactness in point set topology, which has many disadvantages, and the important TNXOHOB product theorem about this compactness is also untenable. Since then, many scholars have put forward various concepts of fuzzy compactness around the discussion of TNXOHOB product theorem, but these compactness are defined for the whole space and are not suitable for general fuzzy subsets, let alone the heredity of closed subsets. In view of this situation, Wang Guojun introduced an ideal fuzzy compactness-good compactness, which was quickly recognized by his colleagues at home and abroad, using the far-field and A-net as tools. Shostaqi, a Soviet mathematical critic, wrote in Achievements in Mathematical Science that good compactness is the most successful fuzzy compactness, which Polish topographer Kubiak called "China compactness".
3. Research on L-fuzzy topology. Wang Guojun's main contribution to L- fuzzy topology is: combining his own concepts and thoughts of molecule, remote domain and ordered homomorphism, he systematically summarized his own and domestic and foreign scholars' work on L- fuzzy topology, and wrote the first monograph on the general theory of L- fuzzy topology space (Shaanxi Normal University Press, 1988). This book starts with the most basic concepts of complete lattice, and describes the construction of complete distributive lattice by using the concepts of minimum set and maximum set. Based on the far field, Moore—Smith convergence theory of molecules is established, continuous order homomorphism and L-fuzzy homeomorphism theory are given, subspace, quotient space and product space are studied, and L-fuzzy topological space and L-fuzzy unit interval generated by topology are introduced. The connectivity, cardinal function, separability, compactness, paracompactness, quasi-uniform structure, degree quantization and adjacent structure theory in L-fuzzy topology are systematically expounded. Many of them are Wang's latest scientific research achievements. Judging from the work in this field at home and abroad, this book really played a fundamental role, and most of the papers published by peer scholars later quoted the contents of this book.
4. The establishment of topological molecular lattice theory. With the development of L-fuzzy topology, Wang put forward the topological lattice theory & topological molecular lattice theory, which is characterized by point set topology and L-fuzzy topology. From the point of view of lattice theory, whether the point set topology developed on {0, 1} x or the (L-) fuzzy topology developed on {0, 1} x or Lx(L is a fuzzy lattice) is a kind of topological theory on lattices, so it can be included in topological lattice theory. However, the traditional topological lattice theory is lacking. Therefore, important local properties such as paracompactness and basic research topics such as embedding theory cannot be discussed. Based on this, Wang Guojun put forward the topological molecular lattice theory in 1979. His basic motivation is to construct a new topological lattice theory, which is quite extensive, including at least point set topology and L-fuzzy topology. At the same time, it retains the point style and fruitful research results of point set topology. In 1985, Wang further improved and generalized this theory and published the paper "Point Topology (Ⅰ, Ⅱ) on Completely Distributive Lattices". At this point, the restriction of inverse operation on lattice has been completely abandoned. Molecule, remote domain and (generalized) ordered homomorphism are three core concepts in topological molecular lattice theory. Molecule is an abstraction of fuzzy points, and far field is a generalization of the concept of heavy field, which is applicable to both cases with and without inverse correspondence. Order homomorphism or generalized order homomorphism is a generalization of Zadeh type function. They ensure that molecules are mapped into molecules, and at the same time, they eliminate the strong condition that Zadeh-type functions keep vertical height. After identification, "Topological Molecular Lattice Theory" was awarded 1985 as an outstanding scientific and technological achievement by the State Education Commission. At the end of 1980s, this theory has formed a preliminary framework, and published a collection of essays in this field, Topological Molecular Lattice Theory, in 1990.
5. Research on fuzzy reasoning and fuzzy logic. Because of the direct application of fuzzy reasoning and fuzzy logic in fuzzy control, it has attracted extensive attention in the fields of fuzzy system and artificial intelligence. Wang Guojun gave a report on "On the Logical Basis of Fuzzy Reasoning" at the International Joint Conference on Information Science held in the United States in March 1997. This report has aroused great interest from many delegates and has been highly praised by many scholars, including former President of the International Association of Fuzzy Systems, Professor Klir of Binghamton University in New York, and famous professors such as Turkson. Professor Moderson, director of the Institute of Fuzzy Systems of Crayton University, also published Wang's full text in the research report of the university. Now this achievement has been published in Information Science. On this basis, Wang put forward the triple Ⅰ method of fuzzy reasoning, which was published in China Science 1999, and improved the traditional CRI method comprehensively. In July 2004, he was elected as the vice chairman of the uncertain mathematics society at the joint meeting of information science held in Salt Lake City, USA.
Professor Wang Guojun pays attention to teaching by example and example. 1983 and 1985 won the teaching quality Excellence Award of Shaanxi Normal University twice, 1985 won the outstanding teacher and advanced worker of Shaanxi Province, and 1993 won the first prize of teachers in normal colleges of Ceng Xianzi Education Foundation. Since 198 1 year. Wang Guojun has trained more than 80 master students, doctoral students and teachers for further study. Some have won the Fok Ying Tung Young Teachers Award in national colleges and universities, some have served as professors and associate professors in their own units, and some have served as department heads, deans or vice-presidents in universities.
Wang Guojun also attached great importance to teaching art, and he clearly advocated that all teachers in normal colleges should be good teachers. Abstract: Classroom teaching is an art. Wang conscientiously summed up his own and others' experiences and lessons in classroom teaching, wrote the article "Ten Taboos in Teaching", and put forward original opinions on the principles, methods and attitudes of classroom teaching. At the beginning of 1992, he edited the book On Teaching Art and won the first prize of excellent teaching achievements in Shaanxi Province.
Although Wang Guojun is now over 70 years old, he still holds a heavy post-graduate teaching job and insists on scientific research. In recent years, he has published more than 65,438+00 academic papers every year. As the ancients said, people over 50 don't study art, which is funded by the Science Publishing Fund of Chinese Academy of Sciences and published by Science Publishing House.
Wang Guojun likes telling stories in his spare time. When telling them, he is lively and interesting, which makes the listeners happy and enlightening. When he was young, he liked singing and expressed his best wishes with beautiful songs. He has always loved sports, especially gymnastics, high jump and table tennis. During his college years, he participated in the first Universiade in Shaanxi Province as a student representative, winning honor for the school. After working in Shaanxi Normal University, he also participated in the table tennis competition for college staff in Shaanxi Province on behalf of the staff. 1996 also participated in the table tennis competition of the department of mathematics and won the championship.
From 65438 to 0960, she married Ms. He in Hanzhong. He Laoshi is also a middle school teacher deeply loved by students. In order to support her husband's career, she took on all the housework and worked as an assistant at work: collecting information, processing letters, sorting books and so on. It saves a lot of time for Wang's teaching and scientific research. Life care and spiritual encouragement are meticulous. They have always loved each other. They have a daughter and two sons, both grown up. My daughter works in Xi 'an, and both sons follow in her stepfather's footsteps. Wang Hao, the eldest son, received his Ph.D. in mathematics from the University of Chicago, and chose computer science when he went to college.