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We obtain map gluing theorems on \(\theta\)-continuity and s\(\theta\)-continuityÂ of maps on topological spaces, in terms of corresponding conditions on the restriction maps to certain subsets of the domain space. Sets containing all the pointsÂ of s \(\theta\) discontinuities and \(\theta\)-discontinuities are obtained. Examples are given to illustrate the necessities of the conditions imposed on the restriction maps.
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