Continuous mappings on subspaces of products with the κ-box topology

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

doi:10.1016/j.topol.2009.04.015

Cited by 7 publications

(7 citation statements)

References 11 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: 83%

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: 83%

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Tkachenko¹

2021

Preprint

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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 [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: 83%

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Tkachenko¹

2021

Axioms

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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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“…Take an arbitrary subset D of G with |D| < 2 τ . Every element f ∈ D is a continuous function on Π ω with values in T. It is clear that the topology of Π ω is the ℵ 1 -box topology of 2 I as defined in [4]. Therefore, we can apply the theorem formulated in the abstract of [4]…”

Section: The Case Of Topological Groupsmentioning

confidence: 99%

The weight and Lindelöf property in spaces and topological groups

Tkachenko

2017

Topology and its Applications

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We show that if Y is a dense subspace of a Tychonoff space X, then w(X) ≤ nw(Y ) N ag (Y ) Better upper bounds for the weight of topological groups are given. For example, if a topological group H contains a dense sub-Several facts about subspaces of Hausdorff separable spaces are established. It is well known that the weight of a separable Hausdorff space X can be as big as 2 2 c . We prove on the one hand that if a regular Lindelöf Σ-space Y is a subspace of a separable Hausdorff space, then w(Y ) ≤ 2 ω , and the same conclusion holds for a Lindelöf P -space Y . On the other hand, we present an example of a countably compact topological group G which is homeomorphic to a subspace of a separable Hausdorff space and satisfies w(G) = 2 2 c , i.e. has the maximal possible weight.

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Continuous mappings on subspaces of products with the κ-box topology

Cited by 7 publications

References 11 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

The weight and Lindelöf property in spaces and topological groups

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