# Generalized linearly ordered spaces and weak pseudocompactness

Oleg Okunev; Angel Tamariz-Mascarúa

Commentationes Mathematicae Universitatis Carolinae (1997)

- Volume: 38, Issue: 4, page 775-790
- ISSN: 0010-2628

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topOkunev, Oleg, and Tamariz-Mascarúa, Angel. "Generalized linearly ordered spaces and weak pseudocompactness." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 775-790. <http://eudml.org/doc/248069>.

@article{Okunev1997,

abstract = {A space $X$ is truly weakly pseudocompact if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove that if $X$ is a generalized linearly ordered space, and either (i) each proper open interval in $X$ is truly weakly pseudocompact, or (ii) $X$ is paracompact and each point of $X$ has a truly weakly pseudocompact neighborhood, then $X$ is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].},

author = {Okunev, Oleg, Tamariz-Mascarúa, Angel},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {weakly pseudocompact spaces; GLOTS; compactifications; weakly pseudocompact space; linearly ordered space},

language = {eng},

number = {4},

pages = {775-790},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Generalized linearly ordered spaces and weak pseudocompactness},

url = {http://eudml.org/doc/248069},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Okunev, Oleg

AU - Tamariz-Mascarúa, Angel

TI - Generalized linearly ordered spaces and weak pseudocompactness

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1997

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 38

IS - 4

SP - 775

EP - 790

AB - A space $X$ is truly weakly pseudocompact if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove that if $X$ is a generalized linearly ordered space, and either (i) each proper open interval in $X$ is truly weakly pseudocompact, or (ii) $X$ is paracompact and each point of $X$ has a truly weakly pseudocompact neighborhood, then $X$ is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].

LA - eng

KW - weakly pseudocompact spaces; GLOTS; compactifications; weakly pseudocompact space; linearly ordered space

UR - http://eudml.org/doc/248069

ER -

## References

top- Eckertson F., Sums, products and mappings of weakly pseudocompact spaces, Topol. Appl. 72 (1996), 149-157. (1996) Zbl0857.54022MR1404273
- Engelking R., General Topology, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
- García-Ferreira S., García-Máynez A.S., On weakly pseudocompact spaces, Houston J. Math. 20 (1994), 145-159. (1994) MR1272568
- Eckertson F., Ohta H., Weak pseudocompactness and zero sets in pseudocompact spaces, manuscript. Zbl0876.54013

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