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- W38142608 abstract "This chapter discusses a characterization of continuously semimetrizable spaces. T space is semimetrizable if there is a real valued function d defined on X2 such that for each x,y ɛ X, d(x,y) = d(y,x) ≥ 0 and d(x,y) = 0 if x = y; and the point p is a limit point of the point set M if for every ε > 0, there is a point x ɛ M distinct from p such that d(p,x) < ε. Such a real valued function d, of course, may be upper semicontinuous, continuous in each variable, or continuous; and there exists a space that admits a semimetric continuous in each variable but none that is upper semicontinuous and a space that admits an upper semicontinuous semimetric continuous in each variable but none that is continuous. A regular space admits an upper semicontinuous semimetric if it is a Moore space and there exists a nondegenerate locally connected Moore space on which all continuous real valued functions is constant. Such a space clearly admits no semimetric that is continuous in each variable." @default.
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- W38142608 date "1977-01-01" @default.
- W38142608 modified "2023-10-16" @default.
- W38142608 title "A CHARACTERIZATION OF CONTINUOUSLY SEMIMETRIZABLE SPACES" @default.
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- W38142608 doi "https://doi.org/10.1016/b978-0-12-584950-0.50013-4" @default.
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