Equimorphy Type of Pairs of Compacta
📜 Abstract
The notion of equimorphy of topological spaces is introduced and the equimorphy type is studied for compact Hausdorff spaces. It is shown that two compact Hausdorff spaces $X$ and $Y$ are equimorphic if and only if they are homeomorphic. The notion of equimorphy is extended to pairs of compacta and also to families of continuous maps, and it is shown that such equimorphy is a special type of homeomorphism. The paper concludes with some open questions about the equimorphy of pairs of compacta.
✨ Summary
The paper “Equimorphy Type of Pairs of Compacta” by P. S. Mostert and Allen L. Shield, published in 1965, explores the concept of equimorphy in the context of topology, specifically focusing on compact Hausdorff spaces. This work introduces equimorphy, investigates its implications, and extends the concept to include pairs of compacta and families of continuous maps. The findings emphasize that equimorphy for compact Hausdorff spaces is equivalent to homeomorphism, thus narrowing down the classification of these spaces by this specific property.
The paper does not seem to have widely recognized direct references in later academic publications or industry applications according to the current records. However, it contributes foundational theoretical insights that support the broader study of topological spaces and provide fodder for subsequent theoretical research in topology. As of the latest searches, no specific modern references were found explicitly citing this paper in influential journals or industrial applications.