Somayeh Soltanpour

Petroleum University of Technology | PUT · Department of Sciences (Ahvaz)

p>Spaces X for which the annihilator of Sλ(X), the λ-super socle of C(X) (i.e., the set of elements of C(X) that cardinality of their cozerosets are less than λ, where λ is a regular cardinal number such that λ≤|X|) is generated by an idempotent are characterized. This enables us to find a topological property equivalent to essentiality of Sλ(X). I...

p> Let $C_c(X)=\{f\in C(X) : |f(X)|\leq \aleph_0\}$, $C^F(X)=\{f\in C(X): |f(X)|<\infty\}$, and $L_c(X)=\{f\in C(X) : \overline{C_f}=X\}$, where $C_f$ is the union of all open subsets $U\subseteq X$ such that $|f(U)|\leq\aleph_0$, and $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$). It is shown that if $X$ is a locally c...