Transitivity of hereditarily metacompact spaces

Hans-Peter A. Künzi

South Africa

University of Cape Town

Dept. Math. and Appl. Math.

Submitted: 2013-12-16

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Accepted: 2013-12-16

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Published: 2003-10-01

DOI: https://doi.org/10.4995/agt.2003.2027
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Keywords:

Point-finite quasi-uniformity, Transitive quasi-uniformity, Transitive topological space, β-space, monotonic β-space, Hereditarily metacompact, Choquet game

Supporting agencies:

Swiss National Science Foundation (under grant 20-63402.00)

Abstract:

We prove that each regular hereditarily metacompact (monotonic) β-space has the property that the third power of any neighbornet belongs to its point-finite quasi-uniformity.

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References:

J. Chaber, On point-countable collections and monotonic properties, Fund. Math. 94 (1977), 209-219.

J. Chaber, M.M. Coban and K. Nagami, On monotonic generalizations of Moore spaces, Cech complete spaces and p-spaces, Fund. Math. 84 (1974), 107-119.

J. Chaber and R. Pol, On hereditarily Baire spaces and σ-fragmentability of mappings and Namioka property, preprint.

P. Fletcher and W.F. Lindgren, Quasi-uniform Spaces, Lecture Notes Pure Appl. Math. 77, Dekker, New York, 1982.

G. Gruenhage, Generalized metric spaces, in: Handbook of Set-theoretic Topology, K. Kunen and J.E. Vaughan, eds., North-Holland Amsterdam, 1984, pp. 423-501.

H.J.K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), 83-108. http://dx.doi.org/10.2140/pjm.1978.76.83

H.J.K. Junnila, H.P.A. Künzi and S. Watson, On a class of hereditarily paracompact spaces, Topology Proc. 25 Summer (2000), 271-289; Russian translation in: Fundam. Prikl. Mat. 4 (1998), 141-154.

H.J.K. Junnila, J.C. Smith and R. Telgársky, Closure-preserving covers by small sets, Topology Appl. 23 (1986), 237-262. http://dx.doi.org/10.1016/0166-8641(85)90042-2

D. König, Sur les correspondances multivoques des ensembles, Fund. Math. 8 (1926), 114-134.

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