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On $\theta$-closed sets and some forms of continuity

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*Mohammad Saleh*

**Address.**

Department of Mathematics,
Birzeit University, P.O. Box 14, West Bank, Palestine

**E-mail. **msaleh@birzeit.edu; salehm@math.ohiou.edu

**Abstract.**

In this paper, we further the study of $\theta $-compactness a
generalization of quasi-H-closed sets and its applications to
some forms of continuity using $\theta $-open and $\delta $-open
sets. Among other results, it is shown a weakly $\theta $-retract
of a Hausdorff space $X$ is a $\delta $-closed subset of $X$.

**AMSclassification. ** 54C08, 54D05, 54D30.

**Keywords. ** Almost closure continuity, $\theta$-open,
$\theta$-closed, quasi-H-closed, S-Hausdorff spaces,
n-compactness.