scholarly journals The countable type properties in free paratopological groups

2017 ◽  
Vol 54 (1) ◽  
pp. 27-41
Author(s):  
Fucai Lin ◽  
Chuan Liu ◽  
Kexiu Zhang
Keyword(s):  
Countable Type

scholarly journals FLAT RING EPIMORPHISMS OF COUNTABLE TYPE

2019 ◽  
Vol 62 (2) ◽  
pp. 383-439 ◽  
Author(s):  
LEONID POSITSELSKI
Keyword(s):  
Associative Ring ◽  
Abelian Category ◽  
Projective Dimension ◽  
Countable Base ◽  
Linear Topology ◽  
Countable Type ◽  
Flat Ring ◽  
Abelian Categories ◽  
Induced Topology ◽  
Strongly Flat

AbstractLet R→U be an associative ring epimorphism such that U is a flat left R-module. Assume that the related Gabriel topology $\mathbb{G}$ of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1. Furthermore, the abelian category of left contramodules over the completion of R at $\mathbb{G}$ fully faithfully embeds into the Geigle–Lenzing right perpendicular subcategory to U in the category of left R-modules, and every object of the latter abelian category is an extension of two objects of the former one. We discuss conditions under which the two abelian categories are equivalent. Given a right linear topology on an associative ring R, we consider the induced topology on every left R-module and, for a perfect Gabriel topology $\mathbb{G}$, compare the completion of a module with an appropriate Ext module. Finally, we characterize the U-strongly flat left R-modules by the two conditions of left positive-degree Ext-orthogonality to all left U-modules and all $\mathbb{G}$-separated $\mathbb{G}$-complete left R-modules.

scholarly journals The Invariant Subspace Problem for Non-Archimedean Banach Spaces

2008 ◽  
Vol 51 (4) ◽  
pp. 604-617 ◽  
Author(s):  
Wiesław Śliwa
Keyword(s):  
Banach Space ◽  
Invariant Subspace ◽  
Banach Spaces ◽  
Continuous Operator ◽  
Linear Continuous Operator ◽  
Infinite Dimensional ◽  
Countable Type ◽  
Closed Invariant Subspace ◽  
Subspace Problem ◽  
Invariant Subspace Problem

AbstractIt is proved that every infinite-dimensional non-archimedean Banach space of countable type admits a linear continuous operator without a non-trivial closed invariant subspace. This solves a problem stated by A. C. M. van Rooij and W. H. Schikhof in 1992.

All tilting modules are of countable type

2006 ◽  
Vol 39 (1) ◽  
pp. 121-132 ◽  
Author(s):  
Jan Šťovíček ◽  
Jan Trlifaj
Keyword(s):  
Tilting Modules ◽  
Countable Type

scholarly journals Products with linear and countable type factors

1997 ◽  
Vol 125 (6) ◽  
pp. 1823-1830 ◽  
Author(s):  
S. Purisch ◽  
M. E. Rudin
Keyword(s):  
Countable Type

A NOTE ON -SPACES

2014 ◽  
Vol 90 (1) ◽  
pp. 144-148
Author(s):  
HANFENG WANG ◽  
WEI HE
Keyword(s):  
Topological Group ◽  
Positive Answer ◽  
Semitopological Group ◽  
Countable Type ◽  
Countable Tightness

AbstractIn this paper, it is shown that every compact Hausdorff $K$-space has countable tightness. This result gives a positive answer to a problem posed by Malykhin and Tironi [‘Weakly Fréchet–Urysohn and Pytkeev spaces’, Topology Appl.104 (2000), 181–190]. We show that a semitopological group $G$ that is a $K$-space is first countable if and only if $G$ is of point-countable type. It is proved that if a topological group $G$ is a $K$-space and has a locally paracompact remainder in some Hausdorff compactification, then $G$ is metrisable.

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