The Justification Logic is a family of logical systems obtained from epistemic logics by adding new type of formulas ^[¯] F\Box F as the interior of F (a topological equivalent of the ‘knowable part of F’). In this paper we extend the Tarski topological interpretation from epistemic modal logics to justification logics which have both: knowledge assertions ^[¯] F\Box F and justification assertions . This topological semantics interprets modality as the interior, terms t represent tests, and a justification assertion represents a part of F which is accessible for test t. We establish a number of soundness and completeness results with respect to Kripke topology and the real line topology for S4-based systems of Justification Logic.