Countably bi-quotient maps and a-spaces

1974 ◽  
pp. 183-189 ◽  
Author(s):  
E. Michael
Keyword(s):  
Quotient Maps

On topological quotient maps preserved by pullbacks or products

1970 ◽  
Vol 67 (3) ◽  
pp. 553-558 ◽  
Author(s):  
B. J. Day ◽  
G. M. Kelly
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Quotient Maps ◽  
Continuous Maps

We are concerned with the category of topological spaces and continuous maps. A surjection f: X → Y in this category is called a quotient map if G is open in Y whenever f−1G is open in X. Our purpose is to answer the following three questions:Question 1. For which continuous surjections f: X → Y is every pullback of f a quotient map?Question 2. For which continuous surjections f: X → Y is f × lz: X × Z → Y × Z a quotient map for every topological space Z? (These include all those f answering to Question 1, since f × lz is the pullback of f by the projection map Y ×Z → Y.)Question 3. For which topological spaces Z is f × 1Z: X × Z → Y × Z a qiptoent map for every quotient map f?

On Topologicalλga-quotient maps

2022 ◽  
Author(s):  
S. Subhalakshmi ◽  
N. Balamani
Keyword(s):  
Quotient Maps

Central extensions and groups locally of minimal type

2015 ◽  
Author(s):  
Brian Conrad ◽  
Gopal Prasad
Keyword(s):  
Root System ◽  
Reductive Group ◽  
Reductive Groups ◽  
Central Extensions ◽  
General Lemma ◽  
Quotient Maps ◽  
Central Quotient ◽  
Characteristic 2 ◽  
Minimal Type ◽  
Quadratic Case

This chapter deals with central extensions and groups locally of minimal type. It begins with a discussion of the general lemma on the behavior of the scheme-theoretic center with respect to the formation of central quotient maps between pseudo-reductive groups; this lemma generalizes a familiar fact in the connected reductive case. The chapter then considers four phenomena that go beyond the quadratic case, along with a pseudo-reductive group of minimal type that is locally of minimal type. It shows that the pseudo-split absolutely pseudo-simple k-groups of minimal type with a non-reduced root system are classified over any imperfect field of characteristic 2. In this classification there is no effect if the “minimal type” hypothesis is relaxed to “locally of minimal type.”

Embeddings and Quotient-Maps

2000 ◽  
pp. 157-186
Author(s):  
Claude-Alain Faure ◽  
Alfred Frölicher
Keyword(s):  
Quotient Maps

scholarly journals Towards an understanding of ramified extensions of structured ring spectra

2018 ◽  
Vol 168 (3) ◽  
pp. 435-454 ◽  
Author(s):  
BJØRN IAN DUNDAS ◽  
AYELET LINDENSTRAUSS ◽  
BIRGIT RICHTER
Keyword(s):  
Hochschild Homology ◽  
Second Order ◽  
Ring Spectra ◽  
Quotient Maps ◽  
Local Complex ◽  
K Theory ◽  
Tame Ramification ◽  
Topological Hochschild Homology

AbstractWe propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the p-local integers. For the tamely ramified extension of the map from the connective Adams summand to p-local complex topological K-theory we determine the relative topological Hochschild homology and show that it detects the tame ramification of this extension. We show that the complexification map from connective topological real to complex K-theory shows features of a wildly ramified extension. We also determine relative topological Hochschild homology for some quotient maps with commutative quotients.

Radical Regularity in Differential Rings

1971 ◽  
Vol 23 (2) ◽  
pp. 197-201 ◽  
Author(s):  
Howard E. Gorman
Keyword(s):  
Jacobson Radical ◽  
Regular Ring ◽  
Prime Ideals ◽  
Differential Ring ◽  
Quotient Maps ◽  
The Stability ◽  
Definition Of ◽  
Finitely Generated Modules ◽  
Regular Rings ◽  
The Ideal

In [1], we discussed completions of differentially finitely generated modules over a differential ring R. It was necessary that the topology of the module be induced by a differential ideal of R and it was natural that this ideal be contained in J(R), the Jacobson radical of R. The ideal to be chosen, called Jd(R), was the intersection of those ideals which are maximal among the differential ideals of R. The question as to when Jd(R) ⊆ J(R) led to the definition of a class of rings called radically regular rings. These rings do satisfy the inclusion, and we showed in [1, Theorem 2] that R could always be “extended”, via localization, to a radically regular ring in such a way as to preserve all its differential prime ideals.In the present paper, we discuss the stability of radical regularity under quotient maps, localization, adjunction of a differential indeterminate, and integral extensions.

Representations of l-Groups by Almost-Finite Quotient Maps

1971 ◽  
Vol 28 (1) ◽  
pp. 59 ◽  
Author(s):  
Donald A. Chambless
Keyword(s):  
Quotient Maps ◽  
Finite Quotient

scholarly journals A non-separable Christensen's theorem and set tri-quotient maps

2009 ◽  
Vol 156 (7) ◽  
pp. 1234-1240 ◽  
Author(s):  
Stoyan Nedev ◽  
Jan Pelant ◽  
Vesko Valov
Keyword(s):  
Quotient Maps

scholarly journals Quotient manifolds of flows

2017 ◽  
Vol 26 (02) ◽  
pp. 1740005 ◽  
Author(s):  
Robert E. Gompf
Keyword(s):  
Euclidean Space ◽  
Vector Fields ◽  
Topological Manifold ◽  
Fundamental Groups ◽  
Smooth Manifolds ◽  
Euclidean Spaces ◽  
Orbit Spaces ◽  
Quotient Maps ◽  
Fixed Dimension

This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of countably presented groups is induced by the quotient map of some flow, and that higher homology can also be controlled. Manifolds of fixed dimension arising as quotients of flows on Euclidean space realize all even (and some odd) intersection pairings, and all homotopy spheres of dimension at least two arise in this manner. Most Euclidean spaces of dimensions five and higher have families of topologically equivalent but smoothly inequivalent flows with quotient homeomorphic to a manifold with flexibly chosen homology. For [Formula: see text], there is a topological flow on (ℝ2r+1 − 8 points) × ℝm that is unsmoothable, although smoothable near each orbit, with quotient an unsmoothable topological manifold.

scholarly journals Convergence quotient maps

1969 ◽  
Vol 65 (2) ◽  
pp. 197-205 ◽  
Author(s):  
D. Kent
Keyword(s):  
Quotient Maps
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