Trivially extending decompositions of en

Research output: Contribution to journalArticlepeer-review


Let G be a monotone decomposition of En, then G can be extended in a trivial way, to the monotone decomposition G1 of En + 1, where En = {{x1 … xn, 0) ∈ En + 1}, by adding to G all points of En + 1 − En. If the decomposition space En/G of G is homeomorphic to En, En\G is said to be obtained by a pseudoisotopy if there exists a map F: En × I→ En × I, such that F t(=f/En × t) is homeomorphism onto En × 1, for all 0 ≦; 1 < 1, F0 is the identity and F1 is equivalent to the projection The purpose of this paper is to present a relation between these two notions. It will then follow, that if G is the decomposition of E3 to points, circles and figure-eights, due to R. H. Bing, for which E3/G is homeomorphic to E3 then E4/G1 is not homeomorphic to E4.

Original languageEnglish
Pages (from-to)727-729
Number of pages3
JournalPacific Journal of Mathematics
Issue number3
StatePublished - Jun 1969
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'Trivially extending decompositions of en'. Together they form a unique fingerprint.

Cite this