We establish that any Hausdorff discretely κ-Lindelöf space X must be κ-Lindelöf if $t(X)\le \kappa$. Besides, in κ-Lindelöf spaces whose tightness does not exceed κ, the property of having pseudocharacter ≤κ must be discretely reflexive. Under the hypothesis $\mathfrak{c}<{\omega }_{\omega }$ we prove that countable pseudocharacter is discretely reflexive in Lindelöf Σ-spaces. If X is a Tychonoff space and $\psi (\bar{D})\le \kappa$ for any discrete set $D\subset C_p(X)$, then ${\kappa }^{+}$ is a caliber of X, we have the inequality $hd(X\times X)\le 2^{\kappa }$ and $\psi (\bar{Y})\le \kappa$ for any $Y\in {[C_p(X)]}^{\le {\kappa }^{+}}$; this implies that $\psi (C_p(X))\le 2^{\kappa }$. We also show that the property of having pseudocharacter ≤κ is discretely reflexive in $C_p(X)$ whenever X is a compact space with $t(X)\le \kappa$.

我们确定任何 Hausdorff 离散κ -Lindelöf 空间X必须是κ -Lindelöf 如果$吨(X)\le \kappa$. 此外，在紧密度不超过κ 的κ -Lindelöf 空间中，具有伪字符≤ κ 的性质必须是离散自反的。根据假设$\mathfrak{C}<{\omega }_{\omega }$我们证明了可数伪字符在 Lindelöf Σ-空间中是离散自反的。如果X是 Tychonoff 空间并且$\psi (\bar{D})\le \kappa$ 对于任何离散集 $D\subset C_{磷}(X)$， 然后 ${\kappa }^{+}$是X的口径，我们有不等式$Hd(X\times X)\le 2^{\kappa }$ 和 $\psi (\overline{是})\le \kappa$ 对于任何 $是\in {[C_{磷}(X)]}^{\le {\kappa }^{+}}$; 这意味着$\psi (C_{磷}(X))\le 2^{\kappa }$. 我们还表明，具有伪字符 ≤ κ的属性在$C_{磷}(X)$每当X是紧致空间时$吨(X)\le \kappa$.