Near metric properties of function spaces

P. Gartside; E. Reznichenko

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 2, page 97-114
  • ISSN: 0016-2736

Abstract

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"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.

How to cite

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Gartside, P., and Reznichenko, E.. "Near metric properties of function spaces." Fundamenta Mathematicae 164.2 (2000): 97-114. <http://eudml.org/doc/212453>.

@article{Gartside2000,
abstract = {"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.},
author = {Gartside, P., Reznichenko, E.},
journal = {Fundamenta Mathematicae},
keywords = {function space; pointwise topology; compact-open topology; cometrisable; stratifiable; compact open topology; Tikhonov space; stratifiable subspace; Polish space},
language = {eng},
number = {2},
pages = {97-114},
title = {Near metric properties of function spaces},
url = {http://eudml.org/doc/212453},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Gartside, P.
AU - Reznichenko, E.
TI - Near metric properties of function spaces
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 2
SP - 97
EP - 114
AB - "Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.
LA - eng
KW - function space; pointwise topology; compact-open topology; cometrisable; stratifiable; compact open topology; Tikhonov space; stratifiable subspace; Polish space
UR - http://eudml.org/doc/212453
ER -

References

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  10. [H] R. W. Heath, A paracompact semi-metric space which is not an M 3 space, Proc. Amer. Math. Soc. 17 (1966), 868-870. Zbl0151.30201
  11. [KV] K. Kunen and J. E. Vaughan, Handbook of Set-Theoretic Topology, North Holland, 1984. 
  12. [McNt] R. A. McCoy and I. Ntantu, Topological Properties of Spaces of Continuous Functions, Lecture Notes in Math. 1315, Springer, 1988. 
  13. [NP] P. J. Nyikos and S. Purisch, Monotone normality and paracompactness in scattered spaces, in: Papers in General Topology and Related Category Theory and Topological Algebra, Ann. New York Acad. Sci. 552, New York Acad. Sci., 1989, 124-137. Zbl0887.54019
  14. [Shk] S. A. Shkarin, preprint. 
  15. [Tk] M. G. Tkachenko, Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. 
  16. [U] V. V. Uspenskiĭ, On the topology of a free locally convex space, Dokl. Akad. Nauk SSSR 270 (1983), 1334-1337. 

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