# Criterion of Normality of the Completely Regular Topology of Separate Continuity

Serdica Mathematical Journal (2006)

- Volume: 32, Issue: 1, page 57-62
- ISSN: 1310-6600

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topGrinshpon, Yakov S.. "Criterion of Normality of the Completely Regular Topology of Separate Continuity." Serdica Mathematical Journal 32.1 (2006): 57-62. <http://eudml.org/doc/281474>.

@article{Grinshpon2006,

abstract = {2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.For given completely regular topological spaces X and Y, there is a completely regular space
X ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuous
if and only if f : X ~⊗ Y→ Z is continuous.
We prove a necessary condition of normality, a sufficient condition of collectionwise normality,
and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.},

author = {Grinshpon, Yakov S.},

journal = {Serdica Mathematical Journal},

keywords = {Separate Continuity; Normality; Collectionwise Normality; Scattered Spaces; Cech-Complete Spaces; Zero-Dimensional Spaces; Paracompactness; Locally Compact Spaces; Separate continuity; normality; collectionwise normality; scattered spaces; Čech-complete spaces; zero-dimensional spaces; paracompactness; locally compact spaces.},

language = {eng},

number = {1},

pages = {57-62},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Criterion of Normality of the Completely Regular Topology of Separate Continuity},

url = {http://eudml.org/doc/281474},

volume = {32},

year = {2006},

}

TY - JOUR

AU - Grinshpon, Yakov S.

TI - Criterion of Normality of the Completely Regular Topology of Separate Continuity

JO - Serdica Mathematical Journal

PY - 2006

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 32

IS - 1

SP - 57

EP - 62

AB - 2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.For given completely regular topological spaces X and Y, there is a completely regular space
X ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuous
if and only if f : X ~⊗ Y→ Z is continuous.
We prove a necessary condition of normality, a sufficient condition of collectionwise normality,
and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.

LA - eng

KW - Separate Continuity; Normality; Collectionwise Normality; Scattered Spaces; Cech-Complete Spaces; Zero-Dimensional Spaces; Paracompactness; Locally Compact Spaces; Separate continuity; normality; collectionwise normality; scattered spaces; Čech-complete spaces; zero-dimensional spaces; paracompactness; locally compact spaces.

UR - http://eudml.org/doc/281474

ER -

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