DearMHFmembers,

I have two questions on Banach spaces,

and I would really appreciate if you help me with acompleteanswer.

Let be a interval and .

- Denote by the set of all real valued bounded functions on ,

whichmayhavejump type discontinuityfrom the left-hand side at the point ,

i.e., and .

Is a Banach space with the norm?- Denote by the set of all real valued bounded functions on ,

whichmayhaveremovable type discontinuityat the point .

Is a Banach space with the norm?

Thanks.

bkarpuz