Abstract
This chapter discusses the behavior of orthocompactness in finite Cartesian products—products with a metric factor and products of ordinals. The results show that the product theory for orthocompactness exhibits striking parallels with that of normality, with metacompactness playing the role of paracompactness. The chapter presents the target theorem to discuss the product theory for orthocompactness. It discusses the preservation of orthocompactness in products with arbitrary metric spaces. One justification for studying the normality of products of ordinals is the well-known fact that every linearly ordered topological space (LOTS) is hereditarily collection-wise normal. Every LOTS is also hereditarily orthocompact and in fact a finite product of ordinals is orthocompact if it is normal.
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