On homeomorphisms of infinite-dimensional bundles. I

Chapman, T. A.; Wong, Raymond Y. T.

doi:10.1090/s0002-9947-1974-0415625-6

Trans. Amer. Math. Soc.

1974

DOI: 10.1090/s0002-9947-1974-0415625-6

|View full text |Cite

On homeomorphisms of infinite-dimensional bundles. I

T. A. Chapman¹,

Raymond Y. T. Wong²

Abstract: ABSTRACT. In this paper we present several aspects of homeomorphism theory in the setting of fibre bundles modeled on separable infinite-dimensional

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1974

1992

Publication Types

Select...

Article6

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 11 publications

(1 citation statement)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. The same as Theorem 1.1 of [7] (see also the remark above). any open cover ll of U by which f is limited, we may choose {g\ to be a ÍU, St"(11))-isotopy.…”

mentioning

confidence: 79%

On homeomorphisms of infinite dimensional bundles. III

Chapman¹,

Wong²

1974

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

ABSTRACT. In this paper we continue the study of homeomorphisms and prove an analogue of the homeomorphism extension theorem for bundles modeled on Hilbert cube manifolds; thus we generalize previous results for Ç-manifolds Hypothesis. Throughout the following let M denote a connected Q-manifold and, for matter of convenience, assume that all spaces considered are metrizable.Our notation and definitions follow that of [7] and [8].2. Separation of sets. We recall that for a bundle E = (E, p, B) and for a pair (F, U) denoting an open set of E and an open cover of F, a (F, ll)-z'soropy ifil on E is a map p = {¡lA: E x I -* E such that pQ -id, each pt is an isomorphism with support in F, and i^.lyl is limited by ll. A closed set K in the product space X x Y is an X-projective Z-set provided the projection of K into X is contained in a closed Z-set of X. A closed subset K of E is a fibre Zset provided K O p~lib) is a Z-set in p~lib) for each b e B. The purpose of this section is to prove the following theorem.

show abstract

“…Proof. The same as Theorem 1.1 of [7] (see also the remark above). any open cover ll of U by which f is limited, we may choose {g\ to be a ÍU, St"(11))-isotopy.…”

mentioning

confidence: 79%

On homeomorphisms of infinite dimensional bundles. III

Chapman¹,

Wong²

1974

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

Fiber Z-sets and fiber rejection homeomorphisms

Банах¹

1992

Math Notes

View full text Add to dashboard Cite

Theory of retracts and infinite-dimensional manifolds

Богатый¹,

Fedorchuk²

1989

J Math Sci

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On homeomorphisms of infinite-dimensional bundles. I

Abstract: ABSTRACT. In this paper we present several aspects of homeomorphism theory in the setting of fibre bundles modeled on separable infinite-dimensional

Cited by 11 publications

References 32 publications

On homeomorphisms of infinite dimensional bundles. III

On homeomorphisms of infinite dimensional bundles. III

Fiber Z-sets and fiber rejection homeomorphisms

Theory of retracts and infinite-dimensional manifolds

Contact Info

Product

Resources

About