Skip to main content

A Characterization of Continuity Revisited

Buy Article:

$20.00 plus tax (Refund Policy)

Abstract:

It is well known that a function f : R → R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2c-dimensional linear spaces of nowhere continuous functions that (except for the zero function) transform compact sets into compact sets and connected sets into connected sets respectively.

Document Type: Short Communication

DOI: http://dx.doi.org/10.4169/amer.math.monthly.118.02.167

Publication date: February 1, 2011

More about this publication?
maa/amm/2011/00000118/00000002/art00009
dcterms_title,dcterms_description,pub_keyword
6
5
20
40
5

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more