Around the equality of small and large inductive dimensions
by
Yasunao Hattori
Shimane University
Coauthors: Vitalij A.Chatyrko, Linköping University

One of the most important facts in dimension theory is the coincidence of ind = Ind = dim for separable metrizable spaces. Roy's famous example and Kulesza's nice example of completely metrizable space X such that ind X = 0 < Ind X show that the metrizability does not work the conincidence of ind = Ind.In this talk, we shall discuss the question : What condition(s) do we need for the conincidence of ind = Ind?We generalize the results of Fitzpatrick-Ford, Mizokami and Fedorchuk.For example, we have the coincidence of the small and large inductive dimensions for the following classes of spaces: (1) Order totally paracompact, strongly hereditarily normal spaces. (2) Order totally paracompact, hereditarily perfectly

Date received: February 24, 2002