Geodesic
The principal kernels of semifields of continuous positive functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 87-107

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This work is devoted to the research of kernel lattices of semifields of continuous positive functions defined on some topological space. It is established that they are lattices with pseudo-complement. New characterizations of the following properties of topological spaces are obtained in terms of kernels, predominantly principal kernels, and semifields of continuous functions: to be an F-space, to be a P-space, basical and extremal disconnectedness, pseudo-compactness, and finiteness. 
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     author = {E. M. Vechtomov and D. V. Chuprakov},
     title = {The principal kernels of semifields of continuous positive functions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {87--107},
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     volume = {14},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a5/}
}
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E. M. Vechtomov; D. V. Chuprakov. The principal kernels of semifields of continuous positive functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 87-107. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a5/