Preservation of properties of a map by forcing

Akira Iwasa

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 1, page 121-129
  • ISSN: 0010-2628

Abstract

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Let f : X Y be a continuous map such as an open map, a closed map or a quotient map. We study under what circumstances f remains an open, closed or quotient map in forcing extensions.

How to cite

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Iwasa, Akira. "Preservation of properties of a map by forcing." Commentationes Mathematicae Universitatis Carolinae 62 63.1 (2022): 121-129. <http://eudml.org/doc/299254>.

@article{Iwasa2022,
abstract = {Let $f\colon X\rightarrow Y$ be a continuous map such as an open map, a closed map or a quotient map. We study under what circumstances $f$ remains an open, closed or quotient map in forcing extensions.},
author = {Iwasa, Akira},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {forcing; open map; closed map; quotient map},
language = {eng},
number = {1},
pages = {121-129},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Preservation of properties of a map by forcing},
url = {http://eudml.org/doc/299254},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Iwasa, Akira
TI - Preservation of properties of a map by forcing
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 1
SP - 121
EP - 129
AB - Let $f\colon X\rightarrow Y$ be a continuous map such as an open map, a closed map or a quotient map. We study under what circumstances $f$ remains an open, closed or quotient map in forcing extensions.
LA - eng
KW - forcing; open map; closed map; quotient map
UR - http://eudml.org/doc/299254
ER -

References

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  4. Iwasa A., Preservation of countable compactness and pseudocompactness by forcing, Topology Proc. 50 (2017), 1–11. MR3488498
  5. Iwasa A., Preservation of a neighborhood base of a set by ccc forcings, Topology Proc. 52 (2018), 61–72. MR3673209
  6. Jech T., Set Theory, The Third Millennium Edition, Revised and Expanded, Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl1007.03002MR1940513
  7. Juhász I., Weiss W., 10.1016/0166-8641(89)90095-3, Topology Appl. 31 (1989), no. 1, 19–27. MR0984101DOI10.1016/0166-8641(89)90095-3
  8. Kunen K., Set Theory: An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing, Amsterdam, 1980. Zbl0534.03026MR0597342

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