Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-vtfg7 Total loading time: 0.202 Render date: 2022-05-28T19:32:06.256Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

A generalized Banach-Mazur theorem

Published online by Cambridge University Press:  17 April 2009

Martin Kleiber
Affiliation:
Villanova University, Villanova, Pa. (USA).
W. J. Pervin
Affiliation:
Drexel Institute of Technology Philadelphia, Pa. 19104 (USA).
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For every infinite cardinal a we let Ca, be the set of all real-valued continuous functions on a product of a closed unit intervals with the supmetric. It is shown that Ca has separability degree a. Further, the classical theorem of Banach and Mazur is generalized by showing that every metric space of separability degree a is isometric to a subspace of ca

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Banach, Stefan, Théorie des opérations linéaires, (Monografie Matematyczne, Warszawa, 1932).Google Scholar
[2]Sierpinski, W., General Topology, (University of Toronto Press, Toronto, 1952).Google Scholar
You have Access
3
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A generalized Banach-Mazur theorem
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A generalized Banach-Mazur theorem
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A generalized Banach-Mazur theorem
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *