# Near metric properties of function spaces

Fundamenta Mathematicae (2000)

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

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topGartside, 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

top- [Bo] C. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16. Zbl0175.19802
- [Bu] R. E. Buck, Some weaker monotone separation and basis properties, Topology Appl. 69 (1996), 1-12. Zbl0848.54015
- [CR] P. J. Collins and A. W. Roscoe, Criteria for metrisability, Proc. Amer. Math. Soc. 90 (1984), 631-640. Zbl0541.54034
- [Du] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367. Zbl0043.38105
- [FGMS]S. Fisher, P. M. Gartside, T. Mizokami and N. Shimane, Near metric properties of hyperspaces, Topology Proc. 22 (1997), 197-211. Zbl0923.54013
- [Ga] P. M. Gartside, Non-stratifiability of topological vector spaces, Topology Appl. 86 (1998), 133-140.
- [Gr1] G. Gruenhage, Generalized metric spaces, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 423-503.
- [Gr2] G. Gruenhage, Generalized metric spaces and metrization, in: Recent Progress in General Topology, North-Holland, 1992, 239-263.
- [Gr3] G. Gruenhage, Cosmicity of cometrizable spaces, Trans. Amer. Math. Soc. 313 (1989), 301-315. Zbl0667.54012
- [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
- [KV] K. Kunen and J. E. Vaughan, Handbook of Set-Theoretic Topology, North Holland, 1984.
- [McNt] R. A. McCoy and I. Ntantu, Topological Properties of Spaces of Continuous Functions, Lecture Notes in Math. 1315, Springer, 1988.
- [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
- [Shk] S. A. Shkarin, preprint.
- [Tk] M. G. Tkachenko, Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37.
- [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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