On 𝑇1- and 𝑇2-productable compact spaces

Abstract

Abstract We prove that if there exists a continuous surjection from a metric compact space 𝑋 onto a product X × T X\times T , where 𝑇 is a T 1 T_{1} second countable topological space which has the cardinality of the continuum, then there exists a surjection from 𝑋 onto the product X × [ 0 , 1 ] X\times[0,1] , where the interval [ 0 , 1 ] [0,1] is equipped with the usual Euclidean topology.