Categorical Aspects of Topology and Analysis Proceedings of an Inter
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915 Categorical Aspects of T apology and Analysis Proceedings of an International Conference Held at Carleton University, Ottawa, August 11-15, 1981
Edited by B. Banaschewski
Spring er-Verlag Berlin Heidelberg New York 1982 1
Editor
B. Banaschewski Mathematical Sciences, McMaster University 1280 Main Street West, Hamilton, Ontario LBS 4K1, Canada
AMS Subject Classifications (1980): 18-06, 18A20, 18A35, 18A40, 18B25, 18B30, 18020, 18F20, 46A12, 46M99, 54E17, 54F05
ISBN 978-3-540-11211-2 Springer-Verlag Berlin Heidelberg New York ISBN 978-0-387-11211-4 Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under§ 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort'', Munich. © by Springer-Verlag Berlin Heidelberg 1982
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
FOREWORD
During the week of August 11, 1981, a conference on categorical aspects of topology and analysis was held at Ottawa, Ontario, Canada, attended by some 70 mathematicians from a dozen different countries.
This volume contains the proceedings thereof,
covering most of the talks presented at the time.
The conference was made financially possible by a grant from the National Science and Engineering Research Council of Canada and a generous contribution from Carleton University.
These and the many additional ways in which Carleton University, and
particularly its Department of Mathematics, assisted the conference are most gratefully acknowledged.
Each paper in this volume has been carefully refereed, and sincere thanks go to all those who contributed their time and energy
to
this task.
CONTENTS
On the largest initial completion of categories of algebra
1
J. Adamek and G.E. Strecker The coreflective hull of the contigual spaces in the category of merotopic spaces
16
H.L. Bentley and H. Herrlich On nuclear limit vector spaces
s.
27
Bjon
Higher order sheaves and Banach modules
40·
F. Borceux On the non-unique extension of topological to bitopological properties
50
G.C.L. Brtlrnmer A categorical approach to probability theory
68
Mich~le Giry Ascoli's theorem for topological categories
86
J.W. Gray Rigid spaces and monoidal closedness
105
G. Greve The Puppe and Nomura operators in the category of homotopy pairs
112
K.A. Hardie and A.V. Jansen Universal completions of concrete categories
127
H. Herrlich Relative nilpotent groups
136
P. Hilton Factorization of cones II, with an application to weak Hausdorff spaces
148
R.E. Hoffmann An essay on free compact groups
171
K.H. Hofmann Spectral dualities involving mixed structures S.S. Hong and L.D. Nel
198
VI Categories of orderable spaces
205
M. Hu°§ek Factorization theorems for geometri
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