A subset of X is I-sequentially compact if and only if it is sequentially countably
compact in the ordinary sense.
Even if this restriction were waived, the number of statements will still be no more than countably
Now we make the additional assumption that X is also countably
ii) strongly countably
compact if every countable cover of X by preopen sets has a finite subcover and countably
P-closed] if every countable cover of X by regular closed [resp: preclosed] sets has a finite subcover.
It is clear, that only for countably
many g we have L([psi] [intersection]g) [not equal to] [empty set].
In this paper we prove that the eigenvalues of the underlying rational eigenproblem can be characterized as minmax values of a Rayleigh functional, from which we immediately obtain the existence of countably
many real and positive eigenvalues.
To do so, we will need to work in the more general setting, Q[[A]], of rational species, that is, of countably
summable linear combinations of molecular species with rational coefficients (v).
[nu]-compact space if every countable [nu]-open cover of it has a finite sub cover.
Example 5 Consider the Hopf algebra QSym of quasisymmetric functions in countably
many variables, and the Hopf subalgebra Sym of symmetric functions.
Siwiec, Sequence-covering and countably
bi-quotient mappings, General Topology Appl.
Second, we propose to derive identities between partitions by looking at suitable ideals in a polynomial ring in countably
many variables endowed with a natural grading.
When P is countably
infinite it is possible for the generating functions we have considered to be irrational.