On simultaneous linear extensions of partial (pseudo)metrics

Extensions of totally bounded pseudometrics

on the effect of linear & non-linear texts on students comprehension and recalling

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N ov 2 00 2 ON SIMULTANEOUS LINEAR EXTENSIONS OF PARTIAL ( PSEUDO ) METRICS

We consider the question of simultaneous extension of (pseudo)metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh’s theorem on linear regular operators extending (pseudo)metrics.

On linear functorial operators extending pseudometrics

For a functor F ⊃ Id on the category of metrizable compacta, we introduce a conception of a linear functorial operator T = {TX : Pc(X) → Pc(FX)} extending (for each X) pseudometrics from X onto FX ⊃ X (briefly LFOEP for F ). The main result states that the functor SP G of G-symmetric power admits a LFOEP if and only if the action of G on {1, . . . , n} has a one-point orbit. Since both the hype...

Counting Linear Extensions of a Partial Order

A partially ordered set (P,<) is a set P together with an irreflexive, transitive relation. A linear extension of (P,<) is a relation (P,≺) such that (1) for all a, b ∈ P either a ≺ b or a = b or b ≺ a, and (2) if a < b then a ≺ b; in other words, a total order that preserves the original partial order. We define Λ(P ) as the set of all linear extensions of P , and define N(P ) = |Λ(P )|. Throu...