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...

homeomorphic to a metric spacePages displaying short descriptions of redirect targets Monotonically normal space – Property of topological spaces stronger than normality...

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

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

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...

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

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

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...

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

information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is...

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

} 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...

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...

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

necessarily satisfies the following properties. F {\displaystyle F\,} is a monotonically non-decreasing, right-continuous function; lim x → − ∞ F ( x ) = 0 ;...

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

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

{\displaystyle (\Omega ,F,P)} is a probability space, with sample space Ω {\displaystyle \Omega } , event space F {\displaystyle F} and probability measure...

Pachner moves are needed. Any arc-presentation of an unknot can be monotonically simplified to a minimal one using elementary moves. So a brute force...

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...

and Y become closer to being perfectly monotonic functions of each other. When X and Y are perfectly monotonically related, the Spearman correlation coefficient...

functions { X n } n ≥ 1 {\displaystyle \{X_{n}\}_{n\geq 1}} converging monotonically (here meaning X n ≤ X n + 1 {\displaystyle X_{n}\leq X_{n+1}} ) and...

asymptote called magnetic saturation. If the magnetic field is now reduced monotonically, M follows a different curve. At zero field strength, the magnetization...

Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like...

is a unimodal function if for some value m, it is monotonically increasing for x ≤ m and monotonically decreasing for x ≥ m. In that case, the maximum value...

is related to x {\displaystyle x} in some manner (such as linearly, monotonically, or perhaps according to some particular functional form such as logarithmic)...

parameter space—for instance a fitted probability being extremely close to zero or one—which results in the Wald test no longer monotonically increasing...

model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference...

classical Fréchet distance without the requirement that the endpoints move monotonically along their respective curves — the dog and its owner are allowed to...