Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Gámez-Merino, José L.
AU - Muñoz-Fernández, Gustavo A.
AU - Seoane-Sepúlveda, Juan B.
TI - A Characterization of Continuity Revisited
JO - American Mathematical Monthly
PY - 2011-02-01T00:00:00///
VL - 118
IS - 2
SP - 167
EP - 170
N2 - 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 2^{c}-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.
UR - http://www.ingentaconnect.com/content/maa/amm/2011/00000118/00000002/art00009
M3 - doi:10.4169/amer.math.monthly.118.02.167
UR - https://doi.org/10.4169/amer.math.monthly.118.02.167
ER -