Cardinal invariants for $\kappa$-box products: weight, density character and Suslin number

Comfort, W. W.; Gotchev, Ivan S.

doi:10.4064/dm748-2-2016

Cited by 2 publications

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“…For example, one can ask whether J ( f ) is a filter or whether it has minimal, by inclusion, elements, or even the smallest element. It has been shown by W. Comfort and I. Gotchev in [7][8][9] that the family J ( f ) can have quite a complicated set-theoretic structure, even if X is a Cartesian product of topological spaces and f is a continuous mapping to a space Y. It is worth mentioning that the thorough study of the family J ( f ) was motivated by a somewhat simpler question on whether J ( f ) had a countable element J ⊂ I.…”

Section: More On Continuous Homomorphisms Of P-modifications Of Products and Their Dense Submonoidsmentioning

confidence: 99%

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Tkachenko¹

2021

Preprint

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We study factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let $D=\prod_{i\in I}D_i$ be a product of paratopological groups, $S$ be a dense subgroup of $D$, and $\chi$ a continuous character of $S$. Then one can find a finite set $E\subset I$ and continuous characters $\chi_i$ of $D_i$, for $i\in E$, such that $\chi=\big(\prod_{i\in E} \chi_i\circ p_i\big)\hs1\res\hs1 S$, where $p_i\colon D\to D_i$ is the projection.

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Section: More On Continuous Homomorphisms Of P-modifications Of Products and Their Dense Submonoidsmentioning

confidence: 99%

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Tkachenko¹

2021

Preprint

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show abstract

“…For example, one can ask whether J ( f ) is a filter or whether it has minimal, by inclusion, elements, or even the smallest element. It has been shown by W. Comfort and I. Gotchev in [19][20][21] that the family J ( f ) can have quite a complicated set-theoretic structure, even if X is a Cartesian product of topological spaces and f is a continuous mapping to a space Y. It is worth mentioning that the thorough study of the family J ( f ) was motivated by a somewhat simpler question on whether J ( f ) had a countable element J ⊂ I.…”

Section: More On Continuous Homomorphisms Of P-modifications Of Products and Their Dense Submonoidsmentioning

confidence: 99%

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Tkachenko¹

2021

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This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let D=∏i∈IDi be a product of paratopological groups, S be a dense subgroup of D, and χ a continuous character of S. Then one can find a finite set E⊂I and continuous characters χi of Di, for i∈E, such that χ=∏i∈Eχi∘piS, where pi:D→Di is the projection.

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Cardinal invariants for $\kappa$-box products: weight, density character and Suslin number

Cited by 2 publications

References 0 publications

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

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