Algebraic operations in Neutrosophic Crisp Sets are diverse, involving multiple types of intersections, unions, complements, and inclusions, which makes the study of their topological properties more complex. This paper investigates neutrosophic crisp compactness and Lindelöf properties within a neutrosophic crisp topological space defined by first-type intersections and second-type unions and complements for all Neutrosophic Crisp Sets. Definitions for compactness and Lindelöfness are introduced based on these operations, and the validity of classical topological theorems is analysed in this context. Comparisons with classical topology reveal that some theorems hold, while others fail, but are valid under specific conditions that have been clarified. This study also examines the impact of specifying algebraic operations on the behaviour of compactness and Lindelöf properties. The theorems that are valid under the proposed framework are rigorously established within the proposed framework. These findings provide new insights into the structure of Neutrosophic Crisp topological spaces and highlight the critical role of algebraic operation selection in determining fundamental.