Equinormality characterizes the compactness (Q1074152)

In this interesting paper, the author proves some results concerning products of syntopogenous spaces in which SP-normality implies compactness. When these results are applied to separated Efremovič proximity spaces one gets the equivalence of the following five statements: (1) (X,\(\delta)\) is compact. (2) The product of (X,\(\delta)\) and its Smirnov compactification \((X^*,\delta^*)\) is equinormal. (3) The product (X\(\times Y\), \(\delta\) \(\times \delta ')\) is equinormal for every compact separated proximity space (Y,\(\delta\) '). (4) \((X^ m,\delta^ m)\) is equinormal, where m is the proximity weight of (X,\(\delta)\). (5) The topology of \((X^ m,\delta^ m)\) is normal for any cardinal number m.