References
Aarnes, J.F.,Continuity of group representations, with applications to C*-algebras, J. Functional Analysis 5 (1970), 14–36.
Arhangel'skii, A.V.,Bicompact sets and the topology of spaces, Trans. Moscow Math. Soc. (1965), 1–62.
—:The closed image of a metric space can be condensed to a metric space, Soviet Math. Dokl. 7 (1966), 1109–1112.
—:Groupes topologiques extrémalement discontinus, C.R. Acad. Sc. Paris A265 (1967), 822–825.
Ball, J.M.,Continuity properties of non-linear semigroups, J. Funct. Analysis 17 (1974), 91–103.
Berglund, J.F. and K.H. Hofmann,Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math. 42, Springer, New York 1967.
Berglund, J.F., H.D. Junghenn and P. Milnes,Compact right topological semigroups and generalizations of almost periodicity, Lecture Notes in Math. 663, Springer-Verlag, New York 1978.
Bourbaki, N.,Éléments de mathématique.Intégration, chap. 8, Hermann, Paris 1963.
—:General topology 2, Addison-Wesley, Reading, Mass. 1966.
Bruhat, F.,Lectures on Lie groups and representations of locally compact groups, Tata Inst. of Fund. Research, Bombay 1958.
Chernoff, P.R.,A note on continuity of semigroups of maps, Proc. Amer. Math. Soc. 53 (1975), 318–320.
Comfort, W.W.,Closed Baire sets are (sometimes) zerosets, Proc. Amer. Math. Soc. 25 (1970), 870–875.
DeLeeuw, K. and I. Glicksberg,The decomposition of certain group representations, J. d'Analyse Math. 15 (1965), 135–192.
Dorroh, J.R.,Semigroups of maps in a locally compact space, Canad. J. Math. 19 (1967), 688–696.
Dunford, N. and J.T. Schwartz,Linear operators I, Interscience Publ., New York 1958.
Dunkl, C.F. and D.E. Ramirez,Representations of commutative semitopological semigroups, Lecture Notes in Math. 435, Springer-Verlag, New York 1975.
Ellis, R.,Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125.
Engelking, R.,Cartesian products and dyadic spaces, Fund. Math. 57 (1965), 287–304.
Fort, M.K. Jr.,Category theorems, Fund. Math. 42 (1955), 276–288.
Gait, J.,The Baire set fixing property in topological groups, Math. Ann. 200 (1973), 235–240.
Grothendieck, A.,Topological vector spaces, Gordon and Breach, New York 1973.
Gulick, D.,Duality theory for the topology of simple convergence, J. Math. Pures et Appl., 52 (1973), 453–472.
Helmer, D.,Continuity of group actions, Dissertation, Tulane Univ., New Orleans 1973.
—:Continuity of locally compact group actions with measurable orbit maps, Math. Zeitschr. 172 (1980), 51–53.
—:Joint continuity of affine semigroup actions, Semigroup Forum 21 (1980), 153–165.
Helmer, D.:Joint continuity of sequentially continuous maps (to appear in Colloq. Math.)
Hewitt, E. and K.A. Ross,Abstract harmonic analysis I, Springer-Verlag, Berlin 1963.
Hofmann, K.H.,Topological semigroups.History, theory, applications, Jber. Dt. Math.-Verein. 78 (1976), 9–59.
—: Review of [16], Bull. Amer. Math. Soc. 83 (1977), 236–243.
—:Compact groups I, Lecture Notes, Tulane Univ., New Orleans 1966-1967.
Iwasawa, K.,On some types of topological groups, Annals of Math. 50 (1949), 507–558.
Kelley, J.L., I. Namioka, et al.,Linear topological spaces, D. van Nostrand, Princeton, N.J. 1963.
Kenderov, P.,Dense strong continuity of pointwise continuous maps, Pacific J. Math. 89 (1980), 111–130.
Köthe, G.,Topological vector spaces I, Springer-Verlag, New York 1969.
Kõmura, T.,Semigroups of operators in locally convex spaces, J. Funct. Analysis 2 (1968), 258–296.
Lawson, J.D.,Joint continuity in semitopological semigroups, Illinois J. Math. 18 (1974), 275–285.
—:Additional notes on continuity in semitopological semigroups, Semigroup Forum 12 (1976), 265–280.
Lee, D.H.,Supplements for the identity component in locally compact groups, Math. Z. 104 (1968), 28–49.
Michael, E.A.,ℵ o -Spaces, J. Math. Mech. 15 (1966), 983–1002.
—:Local compactness and Cartesian products of quotient maps and k-spaces, Ann. Inst. Fourier, Grenoble 18 (1968), 281–286.
Moore, R.T.,Measurable,continuous and smooth vectors for semigroups and group representations, Memoirs Amer. Math. Soc. 78, Providence, R.I. 1968.
Mostert, P.S. and A.L. Shields,Semigroups with identity on a manifold, Trans. Amer. Math. Soc. 91 (1959), 380–389.
Namioka, I.,Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515–531.
—:Right topological groups, distal flows, and a fixed point theorem, Math. Systems Theory 6 (1972), 193–209.
Noble, N., k-spaces and some generalizations, Dissertation, Univ. of Rochester, N.Y. 1967.
Rudin, W.,Functional analysis, McGraw-Hill, New York 1973.
Ruppert, W.,Notes on compact semigroups with identity, Semigroup Forum 14 (1977), 199–234.
—:The structure of semitopological monoids on compact connected manifolds, Math. Zeitschr. 170 (1980), 15–42.
Schwartz, L.,Lectures on mixed problems in partial differential equations and representations of semigroups, Tata Inst. of Fund. Research, Bombay 1957.
Shiga, K.,Representations of a compact group on a Banach space, J. Math. Soc. Japan 7 (1955), 224–248.
Varopoulos, N.Th.,A theorem on the continuity of homomorphisms of locally compact groups, Proc. Camb. Phil. Soc. 60 (1964), 449–463.
Weil, A.,L'intégration dans les groupes topologiques et ses applications, 2. éd. Hermann, Paris 1965.
White, H.E.,Topological spaces in which Blumberg's theorem holds, Proc. Amer. Math. Soc. 44 (1974), 454–462.
Wu, T.-S.,Locally compact semigroups with dense maximal subgroups, Trans. Amer. Math. Soc. 113 (1964), 151–168.
Hille, E. and R.S. Phillips,Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ. XXXI, Providence, R.I. 1957.
Yosida, K.,Functional analysis, Springer-Verlag, New York 1971.
Author information
Authors and Affiliations
Additional information
Communicated by Michael Mislove
Rights and permissions
About this article
Cite this article
Helmer, D. Continuity of semigroup actions. Semigroup Forum 23, 153–188 (1981). https://doi.org/10.1007/BF02676642
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02676642