On the Topological Sets of Larger Cardinalities

• David Delali Zigli
• Vivian Maanu
• Samuel Amoako
• Prince Nimako Gyasi

Topology is one of the active areas of all mathematics. Conventionally, it is considered one of the three areas of pure mathematics, together with algebra and analysis. Formally, if X is a set and τ a family of subsets of X, then τ is a topology on X if both the empty set and X are elements of, τ, any union of elements of τ is an element of, τ and any intersection of finitely many elements of τ is an element of τ. However, checking the topology of a set with cardinality manually is difficult and time-consuming. This study, therefore, introduced a technologically inclined approach (the Python programming language) with a well-developed user-interface for checking the topology of a set or sets with cardinality. The programming language (Python code) was developed using principles of set theory and the definition of the topology of a set. The friendly user-interface developed with the embedded algorithm is able to determine the topology of a set with a larger cardinality and also extract the open and closed sets of the topology, hence making it faster and cheaper.

Select Volume / Issue:

• Volume 9,Issue 1, Jan. 2022

Year:

2022

Type of Publication:

Article

Keywords:

Topological Set; Open Set; Cardinality; Programming; Elements

Journal:

IJASM

Volume:

9

Number:

1

Pages:

16-31

Month:

January

ISSN:

2394-2894