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...

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

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

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...

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...

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...

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

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

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...

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...

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

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

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

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

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

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

} 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...

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

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

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...

statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood...

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

numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions...

to the normal distribution is monotonic, in the sense that the entropy of Z n {\textstyle Z_{n}} increases monotonically to that of the normal distribution...

is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted...

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...

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

{\bmod {1}}>\ln 2} . See for a proof sketch. When the distribution has a monotonically decreasing probability density, then the median is less than the mean...