HOẠT ĐỘNG TRONG TUẦN

Uniform continuity of a product of real functions
Báo cáo viên: Gerald Beer (California State University Los Angeles)

Thời gian: 9h00, Thứ 4 ngày 5/12/2018
Địa điểm: Phòng 302 Nhà A5, Viện Toán học
Tóm tắt: While a product of continuous real-valued functions defined on a metric space must be continuous, the product of a pair of uniformly continuous real functions need not be, even if one is bounded. We give necessary and sufficient conditions for (i) the product of a pair of such functions to be uniformly continuous, and for (ii) the product of an arbitrary pair of such functions to be uniformly continuous, that is, for the vector space of real uniformly continuous functions to form a ring. It is amazing that neither of these basic questions had been resolved until recently.

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