5 problems

Let $(X,\delta)$ be a finite ordinal space and let $n\in\mathbb N^+$. For a subset $A\subseteq X$, write $A\hookrightarrow\mathbb R^n$ when the induced ordinal space on $A$ embeds…

Let $(X,\delta)$ be an ordinal space with $|X|=n\in\mathbb N^+$, and let $x_1,x_2,\ldots,x_n$ be an enumeration of its points satisfying the majorization property. Write…

Let $(X,\delta)$ be an ordinal space with $|X|=n$, and let $\mathbf B_X$ denote its set of balls. Assume that … for every different pairs of points $\{x,y\}\neq\{z,w\}$ with…

Maximal ball-number conjecture. The maximal number of balls in $X$ is $b_n$, where $(b_n)$ is sequence A263511. The paper supports the sequence by direct constructions, including o…

Let $(X,L,\delta)$ be a finite ordinal space. The number of balls means the cardinality of its ball set $\mathbf B_X$. The maximal number is considered over finite ordinal spaces o…