Exploring Hyperconnectedness and Separation in Ideal Topological Spaces
Abstract
We came up with the concept * -open set which has stricter condition with respect to the notion b-open sets, introduced by Andrijevic [3] as a generalization of Levine's [11] generalized closed sets. Anchoring on this concept, we defined * * -hyperconnected sets and * -separated sets. Topology is seen in many areas of science, for example, it is used to model the spacetime notion of the universe. It is sometimes investigated in non-conventional ways, for example Donaldson [7] utilized mathematical concepts used by physicists to solve topological problems. These problems includes new topological sets like * -open set.
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M El-Monsef (1983) -open sets and -continuous mappings. 12, 77-90.
M Abd El-Monsef, A Nasef, A Radwan, F Ibrahem, R Esmaeel Some properties of semi-open sets with respect to an ideal.
D Andrijević (1996) On b-open sets. (205), 59-64.
Michael Baldado (2023) $b^{ast}_{I}$ Sets and $b^{ast}_{I}$-Compact Ideal Spaces. 16(3), 1809-1816.
P Bhattacharyya (1987) Semi Generalized Open Sets and Generalized Semi Closed Sets in Topological Spaces. 29(3), 375-382.
Glaisa T. Catalan, Michael P. Baldado Jr, Roberto N. Padua (2022) βI-Compactness, βI*-Hyperconnectedness and βI-Separatedness in Ideal Topological Spaces.
S Donaldson, P Kronheimer (1990) The geometry of four-manifolds.
E Erdal, N Takashi (2012) *-hyperconnected ideal topological spaces. Analele ştiințifice Ale Universitӑțsi. 121-129.
K Kuratowski (1934) Unknown Title. 40, 787-788.
Norman Levine (1963) Semi-Open Sets and Semi-Continuity in Topological Spaces. 70(1), 36-41.
Norman Levine (1970) Generalized closed sets in topology. 19(1), 89-96.
S Maheshwari, S Thakur (1985) On -compact spaces. 13(4), 341-347.
A Mashhour, M Abd El-Monsef, S El-Deeh (1982) On pre-continuous and weak pre-continuous mappings. 53, 47-53.
S Morris (1989) BAT EARS WITHOUT TEARS. 334(8673), 1193.
A Nasef, A Radwan, R Esmaeel (2015) SOME PROPERTIES OF $alpha$-OPEN SETS WITH RESPECT TO AN IDEAL. 102(4), 613-630.
O Nj_Astad (1965) On some classes of nearly open sets. 15(3), 961-970.
Karishma Shravan, Binod Tripathy (2018) Generalised Closed Sets in Multiset Topological Space. 37(2), 223-237.
K Shravan, B Tripathy (2018) Multiset ideal topological spaces and local functions. 37(4), 699-711.
A Skowron (1989) On topology information systems. 3, 87-90.
M Stone (1937) Applications of the theory of boolean rings to general topology. 41(3), 375-481.
Binod Tripathy, Santanu Acharjee (2014) On (γ,δ)-Bitopological semi-closed set via topological ideal. 33(3), 245-257.
Binod Tripathy, Gautam Ray (2013) Mixed fuzzy ideal topological spaces. 220, 602-607.
R Vaidyanathaswamy (1960) Set topology, chelsea, new york.
Published
2023-10-13
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