Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Transactions of the ...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1991
Data sources: zbMATH Open
Transactions of the American Mathematical Society
Article . 1991 . Peer-reviewed
Data sources: Crossref
Transactions of the American Mathematical Society
Article . 1991 . Peer-reviewed
Data sources: Crossref
versions View all 3 versions
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

First Steps in Descriptive Theory of Locales

First steps in descriptive theory of locales
Authors: Isbell, John;

First Steps in Descriptive Theory of Locales

Abstract

F. Hausdorff and D. Montgomery showed that a subspace of a completely metrizable space is developable if and only if it is F σ {F_\sigma } and G δ {G_\delta } . This extends to arbitrary metrizable locales when " F σ {F_\sigma } " and " G δ {G_\delta } " are taken in the localic sense (countable join of closed, resp. meet of open, sublocales). In any locale, the developable sublocales are exactly the complemented elements of the lattice of sublocales. The main further results of this paper concern the strictly pointless relative theory, which exists because—always in metrizable locales— there exist nonzero pointless-absolute G δ ′ s {G_\delta }’{\text {s}} , G δ {G_\delta } in every pointless extension. For instance, the pointless part pl ( R ) {\text {pl}}({\mathbf {R}}) of the real line is characterized as the only nonzero zero-dimensional separable metrizable pointless-absolute G δ {G_\delta } . There is no nonzero pointless-absolute F σ {F_\sigma } . The pointless part of any metrizable space is, if not zero, second category, i.e. not a countable join of nowhere dense sublocales.

Keywords

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Heyting algebras (lattice-theoretic aspects), pointless part, metrizable locales, complemented sublocales

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    25
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
25
Top 10%
Top 10%
Average
bronze
Beta
sdg_colorsSDGs:
Related to Research communities