• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.919-926
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• 2021

This paper intends to define the metacompact spaces and the D-metacompact spaces as well as study their properties along with their relations with some other topological spaces. Several theoretical results are stated and proved with meticulous care through generalizing many well known theorems concerning with metacompact spaces. These results are supported via handling some illustrative examples.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.471-481
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• 2024

In this paper, the concept of D-sets will be applied to create D-lindelöf spaces, a new type of topological space covering the property. This is performed by using a D-cover, which is a special type of cover. The primary purpose of this work is to introduce the principles and concepts of D-lindelöf spaces. We look into their properties as well as their relationships with other topological spaces. The basic relationship between D-lindelöf spaces and lindelöf spaces, as well as many other topological spaces, will be given and described, including D-compact, D-countably compact, and D-countably lindelöf spaces. Many novel theories, facts, and illustrative and counter-examples will be investigated. We will use several informative instances to explore certain of the features of the Cartesian product procedure across D-lindelöf spaces as well as additional spaces under more conditions.