### LINEAR TO NON-LINEAR TOPOLOGY VIA γ-OPEN SETS IN THE ENVIRONMENT OF BITOPOLOGICAL SPACES

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#### Abstract

Generalizations of open sets always gives a linear structure in an ordinary topological space. This paper proposes that there exists a non-linear structure in a given bitopological space via $\gamma$-open sets of the context. The new structure is also studied in the light of hyperconnectedness to show that it is completely independent with the original one. Also, the relationships between extremally disconnectedness, connectedness and hyperconnectedness are presented in the same environment by means of $\gamma$-open set. Moreover, the idea of maximal $\gamma$-hyperconnectedness is initiated in this work and some important results related to filter, ultrafilter, door space are established. Finally, some functions concerned with $(1, 2) \gamma$-open sets are introduced and interrelationships among them are produced. Some suitable examples and counter examples are properly placed to make the paper self sufficient.

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DOI: https://doi.org/10.22190/FUMI210323061D

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