By Frederic Mynard, Elliott Pearl

The aim of this assortment is to lead the non-specialist during the uncomplicated idea of varied generalizations of topology, beginning with transparent motivations for his or her advent. buildings thought of comprise closure areas, convergence areas, proximity areas, quasi-uniform areas, merotopic areas, nearness and clear out areas, semi-uniform convergence areas, and technique areas. each one bankruptcy is self-contained and obtainable to the graduate scholar, and makes a speciality of motivations to introduce the generalization of topologies thought of, proposing examples the place fascinating homes will not be found in the area of topologies and the matter is remedied within the extra normal context. Then, adequate fabric might be coated to organize the reader for extra complex papers at the subject. whereas classification thought isn't the concentration of the booklet, it's a handy language to review those buildings and, whereas saved as a device instead of an item of analysis, could be used through the e-book. for that reason, the ebook includes an introductory bankruptcy on specific topology

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A 69 = Indag. [75] Math. 28 (1966), 147–160. MR0215766 (35 #6601) , Cat´ egories topologiques. III, Nederl. Akad. Wetensch. Proc. Ser. A 69 = Indag. [76] Math. 28 (1966), 161–175. MR0215766 (35 #6601) [77] , Cat´ egories structur´ ees g´ en´ eralis´ ees, Cahiers Topologie G´eom. Diﬀ´erentielle 10 (1968), 139–167. MR0244337 (39 #5652) [78] T. H. Fay, G. C. L. Br¨ ummer, and K. A. Hardie, A characterization of topological functors, Math. Colloq. Univ. Cape Town 12 (1980) (1978/79), 85–93. MR565148 (81g:18002) [79] W.

Soc. 51 (1955), 254–261. MR0070995 (17,67b) [225] S. Weck-Schwarz, Cartesian closed topological and monotopological hulls: a comparison, Topology Appl. 38 (1991), no. 3, 263–274. MR1098906 (92c:18010) [226] A. Weil, Les recouvrements des espaces topologiques: espaces complets, espaces bicompacts, C. R. Acad. Sci. Paris 202 (1936), 1002–1005. , Sur les espaces a ` structure uniforme et sur la topologie g´ en´ erale, Hermann, Paris, [227] 1937. ˇ [228] O. Wyler, The Stone–Cech compactiﬁcation for limit spaces, Notices Amer.

F. Kennison, Reﬂective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303–315. MR0174611 (30 #4812) [147] D. C. Kent, Convergence quotient maps, Fund. Math. 65 (1969), 197–205. MR0250258 (40 #3497) [148] D. C. Kent and G. D. Richardson, Compactiﬁcations of convergence spaces, Internat. J. Math. Math. Sci. 2 (1979), no. 3, 345–368. -J. Kowalsky, Limesr¨ aume und Komplettierung, Math. Nachr. 12 (1954), 301–340. MR0073147 (17,390b) , Topologische R¨ aume, Lehrb¨ ucher und Monographien aus dem Gebiete der exakten [150] Wissenschaften, Mathematische Reihe, vol.