On the lattice of principal generalized topologies

Arianpoor, Hassan

doi:10.1007/s10998-018-0266-8

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2020

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“…(X, µ) is said to be a strong GTS [3] if X ∈ µ. Research in GTS is still a hot area of research in which researchers introduced several types of continuity, compactness, homogeneity, and sets are extended from ordinary topological spaces to include GTSs in [4][5][6][7][8][9][10][11][12][13][14], and others. As a generalization of bitopological spaces, the author in [15] defined bigeneralized topological space, as follows: an ordered triple (X, σ, δ) of a set X and two generalized topologies σ and δ on X is called a bigeneralized topological space (BGTS).…”

Section: Introductionmentioning

confidence: 99%

On Certain Covering Properties and Minimal Sets of Bigeneralized Topological Spaces

Ghour

Alhorani

2020

Symmetry

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We introduce q-Lindelöf, u-Lindelöf, p-Lindelöf, s-Lindelöf, q-countably-compact, u-countably-compact, p-countably-compact, and s-countably-compact as new covering concepts in bigeneralized topological spaces via q-open sets and u-open sets in bigeneralized topological spaces. Relationships between them are studied. As two symmetries relationships, we show that q-Lindelöf and u-Lindelöf are equivalent concepts, and that q-countably-compact and u-countably-compact are equivalent concepts. We focus on continuity images of these covering properties. Finally, we define and investigate minimal q-open set, minimal u-open set, and minimal s-open sets as three new types of minimality in bigeneralized topological spaces.

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