The embeddability ordering of topological spaces

Representing Quasi-orders by Embeddability Ordering of Families of Topological Spaces

An elementary argument constructs, for each cardinal α, a topological space whose subspaces, ordered by homeomorphic embeddability, can model every partial order on α-many points. We show how to modify this procedure to deal also with quasi-orders (where the antisymmetry condition may fail), obtaining an initial estimate of the cardinality of the space then required.

The topological ordering of covering nodes

The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

Testing Embeddability Between Metric Spaces

Let L ≥ 1, > 0 be real numbers, (M,d) be a finite metric space and (N, ρ) be a metric space (Rudin 1976). The metric space (M,d) is said to be Lbilipschitz embeddable into (N, ρ) if there is an injective function f :M → N with 1/L · d(x, y) ≤ ρ(f(x), f(y)) ≤ L · d(x, y) for all x, y ∈ N (Farb & Mosher 1999, David & Semmes 2000, Croom 2002). In this paper, we also say that (M,d) is -far from bei...

Coarse embeddability into Banach spaces

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.