equivalent formulations for continuity
If is open in , then is open in .
If is closed in , then is closed in .
for all .
Whenever two nets and in converge to the same point, then and converge to the same point in .
If is a filter on that converges to , then is a filter on that converges to . Here, is the filter generated by the filter base .
If is any element of a basis for the topology of , then is open in .
If , and is any neighborhood of , then is a neighborhood of .
is continuous at every point in .
|Title||equivalent formulations for continuity|
|Date of creation||2013-03-22 15:18:23|
|Last modified on||2013-03-22 15:18:23|
|Last modified by||matte (1858)|