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specifically in the field of topology, a monotonically normal space is a particular kind of normal space, defined in terms of a monotone normality operator...

space – Property of topological spaces stronger than normality Monotonically normal space – Property of topological spaces stronger than normality Willard...

called monotonic if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does...

metrizable spaces are collectionwise normal and being metrizable is a hereditary property. Every monotonically normal space Engelking, Theorem 5.1.17, shows...

Collectionwise normal space – Property of topological spaces stronger than normality Locally normal space Monotonically normal space – Property of topological...

that a compact topological space is the continuous image of a total order if and only if it is a monotonically normal space. Nikiel, J. (1986). "Some problems...

targets Monotonically normal space – Property of topological spaces stronger than normality Normal space – Type of topological space Paranormal space Čech...

imply that function and its derivatives are alternately monotonically increasing and monotonically decreasing functions. Such functions were first studied...

91001. Heath, R. W.; Lutzer, David J.; Zenor, P. L. (1973). "Monotonically normal spaces". Transactions of the American Mathematical Society. 178: 481–493...

particularly functional analysis, the Helly space, named after Eduard Helly, consists of all monotonically increasing functions ƒ : [0,1] → [0,1], where...

Euclidean space), several curvatures are defined, which relates the direction of curvature to the surface's unit normal vector, including the: normal curvature...

that is topologically equivalent. This can be done using a subadditive monotonically increasing bounded function which is zero at zero, e.g. d ′ ( x , y...

} We would show that with respect to this mu operator, the space is monotonically normal. Note that μ ( x , G ) ⊆ G . {\displaystyle \mu (x,G)\subseteq...

or planets, to form. Since the Big Bang, the universe has expanded monotonically. Perhaps unsurprisingly, our universe has just the right mass–energy...

In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations...

1984. Williams, Scott W.; Zhou, Haoxuan Order-like structure of monotonically normal spaces. Comment. Math. Univ. Carolin. 39 (1998), no. 1, 207–217. Pelant...

International Space Station led to depression, sleep disorders, and diminished personal interactions, likely due to confined spaces and the monotony and boredom...

each choice of the embedded points x i {\displaystyle x_{i}} and is a monotonically increasing function f {\displaystyle f} , define the "stress" function:...

number of modes in each one-third of an octave. The curve increases monotonically (each one-third of an octave must have more modes than the preceding...

since we have assumed that r′ ≠ 0, it follows that s(t) is a strictly monotonically increasing function. Therefore, it is possible to solve for t as a function...