# Selections that characterize topological completeness

Jan van Mill; Jan Pelant; Roman Pol

Fundamenta Mathematicae (1996)

- Volume: 149, Issue: 2, page 127-141
- ISSN: 0016-2736

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topvan Mill, Jan, Pelant, Jan, and Pol, Roman. "Selections that characterize topological completeness." Fundamenta Mathematicae 149.2 (1996): 127-141. <http://eudml.org/doc/212112>.

@article{vanMill1996,

abstract = {We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].},

author = {van Mill, Jan, Pelant, Jan, Pol, Roman},

journal = {Fundamenta Mathematicae},

keywords = {selection; Vietoris topology; completely metrizable; completely metrizable space},

language = {eng},

number = {2},

pages = {127-141},

title = {Selections that characterize topological completeness},

url = {http://eudml.org/doc/212112},

volume = {149},

year = {1996},

}

TY - JOUR

AU - van Mill, Jan

AU - Pelant, Jan

AU - Pol, Roman

TI - Selections that characterize topological completeness

JO - Fundamenta Mathematicae

PY - 1996

VL - 149

IS - 2

SP - 127

EP - 141

AB - We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].

LA - eng

KW - selection; Vietoris topology; completely metrizable; completely metrizable space

UR - http://eudml.org/doc/212112

ER -

## References

top- [1] M. M. Čoban and E. A. Michael, Representing spaces as images of zero-dimensional spaces, Topology Appl. 49 (1993), 217-220.
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- [9] K. Kunen, Set Theory. An Introduction to Independence Proofs, Stud. Logic Found. Math. 102, North-Holland, Amsterdam, 1980.
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- [11] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143-178. Zbl0222.02075
- [12] E. A. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238. Zbl0070.39502
- [13] E. A. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 656-674.
- [14] J. van Mill and E. Wattel, Selections and orderability, Proc. Amer. Math. Soc. 83 (1981), 601-605. Zbl0473.54010
- [15] A. H. Stone, On σ-discreteness and Borel isomorphism, Amer. J. Math. 85 (1963), 655-666. Zbl0117.40103

## Citations in EuDML Documents

top- Valentin Gutev, Consonance and Cantor set-selectors
- I. Stasyuk, Edward D. Tymchatyn, A continuous operator extending ultrametrics
- Angel Tamariz-Mascarúa, Continuous selections on spaces of continuous functions
- Bohuslav Balcar, Vladimír Müller, Jaroslav Nešetřil, Petr Simon, Jan Pelant (18.2.1950–11.4.2005)
- Bohuslav Balcar, Vladimír Müller, Jaroslav Nešetřil, Petr Simon, Jan Pelant (18.2.1950–11.4.2005)

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