This is an expositive paper reflecting certain viewpoint of intuitionists for the structure of continuum. What we provide is a descriptive theory for Poincaré-type continuum whose first hyperstandard model （PC）...This is an expositive paper reflecting certain viewpoint of intuitionists for the structure of continuum. What we provide is a descriptive theory for Poincaré-type continuum whose first hyperstandard model （PC） was given previously^[3]. Here we construct a new hyperstandard model [PC] instead of （PC）, and present three propositions related to the concept of semi-infinitesimal. Finally, an application of R （non-Cantorian continuum） in Calculus is expounded.Keywords Poincar6＇s intimate bond （IB）; hyperstandard microinterval; semi-infinitesimal; non-punctiform element.展开更多
基金supported in part by NSFC(No.11131003,No.11626245)the "985" Project from the Ministry of Education in Chinathe Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This is an expositive paper reflecting certain viewpoint of intuitionists for the structure of continuum. What we provide is a descriptive theory for Poincaré-type continuum whose first hyperstandard model （PC） was given previously^[3]. Here we construct a new hyperstandard model [PC] instead of （PC）, and present three propositions related to the concept of semi-infinitesimal. Finally, an application of R （non-Cantorian continuum） in Calculus is expounded.Keywords Poincar6＇s intimate bond （IB）; hyperstandard microinterval; semi-infinitesimal; non-punctiform element.
