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Spaces with an M-diagonal

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this note we prove that if X is a Tychonoff space and \(X^2 {\setminus }\Delta \) is dominated by a second countable space then X is cosmic. This solves an open problem of Cascales et al. (Topol Appl 158:204–214). We also consider the case when X is compact and \(X^2 {\setminus }\Delta \) is dominated by a metric space M; in this situation we show that if such domination is strong, then the tightness of X is bounded by the weight of M.

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Acknowledgements

The author wishes to dedicate the present paper to the memory of the late Professor Bernardo Cascales Salinas, outstanding mathematician mentor and friend. The author also thanks professors Z. Feng, J. Orihuela, V. Tkachuk and the anonymous referee for their most valuable comments and remarks on the contents of this note.

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  1. Universidad Autonoma Metropolitana Iztapalapa, Mexico City, Mexico

    David Guerrero Sánchez

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  1. David Guerrero Sánchez
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Correspondence to David Guerrero Sánchez.

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Sánchez, D.G. Spaces with an M-diagonal. RACSAM 114, 16 (2020). https://doi.org/10.1007/s13398-019-00745-x

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