The embeddability ordering of topological spaces Article

Comfort, WW, Gillam, WD. (2006). The embeddability ordering of topological spaces . TOPOLOGY AND ITS APPLICATIONS, 153(13), 2192-2198. 10.1016/j.topol.2004.02.023

cited authors

  • Comfort, WW; Gillam, WD



  • For K a set of topological spaces and X, Y ∈ K, the notation X ⊆h Y means that X embeds homeomorphically into Y; and X ∼ Y means X ⊆h Y ⊆h X. With over(X, ̃) : = {Y ∈ K : X ∼ Y}, the equivalence relation ∼ on K induces a partial order ≤h well-defined on K / ∼ as follows: over(X, ̃) ≤h over(Y, ̃) if X ⊆h Y. For posets (P, ≤P) and (Q, ≤Q), the notation (P, ≤P) {right arrow, hooked} (Q, ≤Q) means: there is an injection h : P → Q such that p0 ≤P p1 in P if and only if h (p0) ≤Q h (p1) in Q. For κ an infinite cardinal, a poset (Q, ≤Q) is a κ-universal poset if every poset (P, ≤P) with | P | ≤ κ satisfies (P, ≤P) {right arrow, hooked} (Q, ≤Q). The authors prove two theorems which improve and extend results from the extensive relevant literature. {A formulation is presented} {A formulation is presented}. © 2005 Elsevier B.V. All rights reserved.

publication date

  • July 1, 2006

published in

Digital Object Identifier (DOI)

start page

  • 2192

end page

  • 2198


  • 153


  • 13