Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An embedding space triple of the unit interval into a graph and its bundle structure


Author: Katsuro Sakai
Journal: Proc. Amer. Math. Soc. 111 (1991), 1171-1175
MSC: Primary 57N20; Secondary 58D05, 58D15
MathSciNet review: 1037222
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {l_2}$ denote a Hilbert space, and let

$\displaystyle l_2^Q = \{ ({x_i}) \in {l_2}\vert\sup \vert i \cdot {x_i}\vert < ... ...^f = \{ ({x_i}) \in {l_2}\vert{x_i} = 0{\text{ except for finitely many }}i\} .$

We show that the triple $ (H(X),{H^{{\text{LIP}}}}(X),{H^{{\text{PL}}}}(X))$ of spaces of homeomorphisms, of Lipschitz homeomorphisms, and of PL homeomorphisms of a finite graph $ X$ onto itself is an $ ({l_2},l_2^Q,l_2^f)$-manifold triple, and that the triple $ (E(I,X),{E^{{\text{LIP}}}}(I,X),{E^{{\text{PL}}}}(I,X))$ of spaces of embeddings, of Lipschitz embeddings, and of PL embeddings of $ I = [0,1]$ into a graph $ X$ is an $ ({l_2},l_2^Q,l_2^4)$-manifold triple.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N20, 58D05, 58D15

Retrieve articles in all journals with MSC: 57N20, 58D05, 58D15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1037222-X
PII: S 0002-9939(1991)1037222-X
Keywords: $ ({l_2},l_2^Q,l_2^f)$-manifold triple, graph, space of homeomorphisms, Lipschitz homeomorphism, PL homeomorphism, space of embeddings, Lipschitz embedding, PL embedding, space of arcs, local trivial bundle
Article copyright: © Copyright 1991 American Mathematical Society