On the functor of semiadditive τ-smooth functionals

Beshimov, R. B.; Mamadaliev, N. K.

doi:10.1016/j.topol.2017.02.037

Cited by 7 publications

(2 citation statements)

References 2 publications

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“…In recent researches an interest in the theory of cardinal invariants and their behavior under the influence of various covariant functors is increasing fast. In [2][3][4][5]9] the authors investigated several cardinal invariants under the influence of some weakly normal and normal functors and hyperspaces.…”

Section: Introductionmentioning

confidence: 99%

On τ-bounded spaces and hyperspaces

Beshimov

Georgiou

Mamadaliev

2022

Filomat

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In this paper, we prove facts and properties on ?-bounded spaces, which are introduced in [10]. More precisely, we prove that an arbitrary product of ?-bounded spaces is ? bounded and vice versa, and that the ?-bounded property is preserved by ?-continuous maps. In particular, continuous maps preserve ?-bounded spaces. Moreover, we investigate the behavior of the minimal tightness and functional tightness of topological spaces under the influence of an exponential functor of finite degree. It is proved that this functor preserves the functional tightness and the minimal tightness of compact sets.

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Section: Introductionmentioning

confidence: 99%

On τ-bounded spaces and hyperspaces

Beshimov

Georgiou

Mamadaliev

2022

Filomat

Self Cite

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“…In [7], the topological properties of topological groups were studied. In [5], categorical and topological properties of the functor OS τ of semiadditive τ -smooth functionals in the category T ych of Tychonoff spaces and their continuous mappings, which extends the functors OS of semiadditive functionals in the category Comp of compact and their continuous mappings, were investigated.…”

Section: Introductionmentioning

confidence: 99%

Index boundedness and uniform connectedness of space of the G-permutation degree

2021

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In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);(2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open);(3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.

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Categorical and topological properties of the functor of Radon functionals

Beshimov

Mamadaliev

2020

Topology and its Applications

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On the functor of semiadditive τ-smooth functionals

Cited by 7 publications

References 2 publications

On τ-bounded spaces and hyperspaces

On τ-bounded spaces and hyperspaces

Index boundedness and uniform connectedness of space of the G-permutation degree

Categorical and topological properties of the functor of Radon functionals

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