Skip to main content
SpringerLink
Log in

Subfit, Fit, Open and Complete

  • Chapter
  • First Online:
Separation in Point-Free Topology

  • 442 Accesses

Abstract

In this final chapter, after briefly summarizing some of the already discussed facts concerning subfitness and fitness, we will tackle an aspect of these properties we have not examined yet, the role they play in the links of the phenomena of completeness, openness and the Heyting structure. Let us explain the main topic we will be interested in.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    To add a further example, not treated here, see [132], where the role of subfitness in combination with the property of monotone normality is studied.

  2. 2.

    Compare it with formula E Y = {(U, V ) | U ∩ Y = V ∩ Y } from I.5.3 representing a subspace Y  of a topological space X as a congruence in Ω(X).

References

  1. T. Dube. A note on weakly pseudocompact locales. Appl. Gen. Topol. 18 (2017) 131–141.

    Article  MathSciNet  Google Scholar 

  2. J. Gutiérrez García, J. Picado, M. A. de Prada Vicente. Monotone normality and stratifiability from a pointfree point of view. Topology Appl. 168 (2014) 46–65.

    Article  MathSciNet  Google Scholar 

  3. J. R. Isbell. Atomless parts of spaces. Math. Scand. 31 (1972) 5–32.

    Article  MathSciNet  Google Scholar 

  4. A. Joyal, M. Tierney. An Extension of the Galois Theory of Grothendieck. Mem. Amer. Math. Soc., vol. 309. Amer. Math. Soc., Providence, RI, 1984.

    Google Scholar 

  5. J. Picado, A. Pultr. Frames and Locales: Topology without points. Frontiers in Mathematics, vol. 28, Springer, Basel, 2012.

    Google Scholar 

  6. J. Picado, A. Pultr, A. Tozzi. Ideals in Heyting semilattices and open homomorphisms. Quaestiones Math. 30 (2007) 391–405.

    Article  MathSciNet  Google Scholar 

  7. A. Simpson. Measure, randomness and sublocales. Ann. Pure Appl. Logic 163 (2012) 1642–1659.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal

    Jorge Picado

  2. Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Aleš Pultr

Authors
  1. Jorge Picado
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aleš Pultr
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Picado, J., Pultr, A. (2021). Subfit, Fit, Open and Complete. In: Separation in Point-Free Topology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-53479-0_10

Download citation

Publish with us

Policies and ethics

Search

Navigation