EUDML

For a functor $F \supset I d$ on the category of metrizable compacta, we introduce a conception of a linear functorial operator $T = {T_{X} : P c (X) \to P c (F X)}$ extending (for each $X$ ) pseudometrics from $X$ onto $F X \supset X$ (briefly LFOEP for $F$ ). The main result states that the functor $S P_{G}^{n}$ of $G$ -symmetric power admits a LFOEP if and only if the action of $G$ on ${1, \dots, n}$ has a one-point orbit. Since both the hyperspace functor $exp$ and the probability measure functor $P$ contain $S P^{2}$ as a subfunctor, this implies that both $exp$ and $P$ do not admit LFOEP.

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Breaking symmetry on complete bipartite graphs of odd size.

Degree sequences of $F$ -free graphs.

Integer sets having the maximum number of distinct differences.

The Turán density of the hypergraph ${a b c, a d e, b d e, c d e}$ .

Correction to the paper: On linear functorial operators extending pseudometrics

On linear functorial operators extending pseudometrics