Weakly weighted generalised quasi-metric spaces and semilattices
Authors: 
Ilaria Castellano, Anna Giordano Bruno, and Nicolò ZavaAuthors Info & Claims
Ilaria Castellano, Anna Giordano Bruno, and Nicolò ZavaAuthors Info & ClaimsReferences
[1]
S. Abramsky, A. Jung, Domain theory, in: Handbook of Logic in Computer Science, vol. 3, in: Handb. Log. Comput. Sci., vol. 3, Oxford Sci. Publ., Oxford Univ. Press, New York, 1994, pp. 1–168.
[2]
R.L. Adler, A.G. Konheim, M.H. McAndrew, Topological entropy, Trans. Am. Math. Soc. 114 (1965) 309–319.
[3]
S. Assaf, K. Pal, Partial metric spaces with negative distances and fixed point theorems, Topol. Proc. 49 (2017) 19–40.
[4]
F. Ayatollah Zadeh Shirazi, D. Dikranjan, Set-theoretical entropy: a tool to compute topological entropy, in: Proceedings ICTA2011 Islamabad Pakistan July 4–10 2011, Cambridge Scientific Publishers, 2012, pp. 11–32.
[5]
G. Birkhoff, Lattice Theory, American Mathematical Society, New York, 1940.
[6]
M.A. Bukatin, J.S. Scott, Towards computing distances between programs via Scott domains, in: S. Adian, A. Nerode (Eds.), Logical Foundation of Computer Science, in: Lecture Notes in Computer Science, vol. 1234, Springer, Berlin, 1997, pp. 33–43.
[7]
M.A. Bukatin, S.Y. Shorina, Partial metrics and co-continuous valuations, in: Foundations of Software Science and Computation Structures, in: Lecture Notes in Comput. Sci., vol. 1378, Lisbon, 1998, Springer, Berlin, 1998, pp. 125–139.
[8]
I. Castellano, A. Giordano Bruno, Algebraic entropy in locally linearly compact vector spaces, in: Rings, Polynomials, and Modules, Springer, 2017, pp. 103–127.
[9]
I. Castellano, A. Giordano Bruno, Topological entropy for locally linearly compact vector spaces, Topol. Appl. 252 (2019) 112–144.
[10]
I. Castellano, D. Dikranjan, D. Freni, A. Giordano Bruno, D. Toller, Intrinsic entropy for generalised quasimetric semilattices, J. Algebra Appl. 21 (10) (2022) 24 pp.
[11]
D. Dikranjan, A. Giordano Bruno, Topological entropy and algebraic entropy for group endomorphisms, in: Proceedings ICTA2011 Islamabad Pakistan July 4–10 2011, Cambridge Scientific Publishers, 2012, pp. 133–214.
[12]
D. Dikranjan, A. Giordano Bruno, The Bridge Theorem for totally disconnected LCA groups, Topol. Appl. 169 (2014) 21–32.
[13]
D. Dikranjan, A. Giordano Bruno, Entropy on abelian groups, Adv. Math. 298 (2016) 612–653.
[14]
D. Dikranjan, A. Giordano Bruno, Entropy on normed semigroups, Diss. Math. 542 (2019) 1–90.
[15]
D. Dikranjan, A. Giordano Bruno, H.-P. Künzi, N. Zava, D. Toller, Generalized quasi-metric semilattices, Topol. Appl. 309 (2022) 35 pp.
[16]
D. Dikranjan, A. Giordano Bruno, L. Salce, Adjoint algebraic entropy, J. Algebra 324 (3) (2010) 442–463.
[17]
D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (7) (2015) 2933–2961.
[18]
D. Dikranjan, B. Goldsmith, L. Salce, P. Zanardo, Algebraic entropy for abelian groups, Trans. Am. Math. Soc. 361 (7) (2009) 3401–3434.
[19]
D. Dikranjan, I. Protasov, N. Zava, Hyperballeans of groups, Topol. Appl. 263 (2019) 172–198.
[20]
I. Eidhammer, I. Jonassen, W.R. Taylor, Protein Bioinformatics: An Algorithmic Approach to Sequence and Structure Analysis, John Wiley & Sons Ltd, West Sussex, England, 2004.
[21]
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, D.S. Scott, Continuous Lattices and Domains, Encyclopedia Math. Appl., vol. 93, Cambridge University Press, Cambridge, 2003.
[22]
A. Giordano Bruno, Adjoint entropy vs Topological entropy, Topol. Appl. 159 (9) (2012) 2404–2419.
[23]
A. Giordano Bruno, M. Shlossberg, D. Toller, Algebraic entropy on strongly compactly covered groups, Topol. Appl. 263 (2019) 117–140.
[24]
A. Giordano Bruno, S. Virili, Topological entropy in totally disconnected locally compact groups, Ergod. Theory Dyn. Syst. 37 (7) (2017) 2163–2186.
[25]
B. Goldsmith, K. Gong, On adjoint entropy of abelian groups, Commun. Algebra 40 (3) (2012) 972–987.
[26]
J. Goubault-Larrecq, Non-Hausdorff Topology and Domain Theory, Selected Topics in Point-Set Topology, New Mathematical Monographs, Cambridge University Press, Cambridge, 2013.
[27]
F. Hausdorff, Grundzüge der Mengenlehre, Leipzig, 1914.
[28]
B.M. Hood, Topological entropy and uniform spaces, J. Lond. Math. Soc. (2) 8 (1974) 633–641.
[29]
A.N. Kolmogorov, New metric invariants of transitive dynamical systems and automorphisms of Lebesgue spaces, Dokl. Akad. Nauk SSSR 119 (1958) 861–864.
[30]
H.-P. Künzi, V. Vajner, Weighted quasi-metrics, in: Papers on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, Flushing, NY, 1992, New York Acad. Sci., New York, 1994, pp. 64–77.
[31]
M. O'Keeffe, S. Romaguera, M. Schellekens, Norm-weightable Riesz spaces and the dual complexity space, Electron. Notes Theor. Comput. Sci. 74 (2003) 105–121.
[32]
S.J. O'Neill, Partial metrics, valuations, and domain theory, in: Papers on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 806, Gorham, ME, 1995, New York Acad. Sci., New York, 1996, pp. 304–315.
[33]
S.G. Matthews, Partial metric topology, in: Papers on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, Flushing, NY, 1992, New York Acad. Sci., New York, 1994, pp. 183–197.
[34]
Y. Nakamura, Entropy and semivaluations on semilattices, Kodai Math. Semin. Rep. 22 (1970) 443–468.
[35]
S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topol. Appl. 98 (1999) 311–322.
[36]
L. Salce, P. Zanardo, A general notion of algebraic entropy and the rank entropy, Forum Math. 21 (4) (2009) 579–599.
[37]
M.P. Schellekens, The Smyth completion: a common foundation for denotational semantics and complexity analysis, in: Proc. MFPS 11, in: Electronic Notes in Theoretical Computer Science, vol. I, Elsevier, 1995, pp. 211–232.
[38]
M.P. Schellekens, On upper weighted spaces, in: Proc. 11th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 806, 1996, pp. 348–363.
[39]
M.P. Schellekens, Extendible spaces, Appl. Gen. Topol. 3 (2) (2002) 169–184.
[40]
M.P. Schellekens, The correspondence between partial metrics and semivaluations, Theor. Comput. Sci. 315 (1) (2004) 135–149.
[41]
D. Scott, A type theoretic alternative to ISWIM, CUCH, OWHY, manuscript University of Oxford, 1969.
[42]
D. Scott, Outline of a mathematical theory of computation, in: 4th Annual Princeton Conference on Information Sciences and Systems, 1970, pp. 169–176.
[43]
C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (3) (1948) 379–423.
[44]
Y.G. Sinai, On the concept of entropy of a dynamical system, Dokl. Akad. Nauk SSSR 124 (1959) 768–771.
[45]
S. Virili, Entropy for endomorphisms of LCA groups, Topol. Appl. 159 (9) (2012) 2546–2556.
[46]
H. Weber, Uniform lattices I: a generalization of topological Riesz spaces and topological Boolean rings, Ann. Mat. Pura Appl. (4) 160 (1991) 347–370. 1992.
[47]
H. Weber, Uniform lattices II: order continuity and exhaustivity, Ann. Mat. Pura Appl. (4) 165 (1993) 133–158.
[48]
M.D. Weiss, Algebraic and other entropies of group endomorphisms, Math. Syst. Theory 8 (3) (1974/75) 243–248.
[49]
W.A. Wilson, On quasi-metric spaces, Am. J. Math. 53 (3) (1931) 675–684.
[50]
N. Zava, Generalisations of coarse spaces, Topol. Appl. 263 (2019) 230–256.
Index Terms
- Weakly weighted generalised quasi-metric spaces and semilattices
Index terms have been assigned to the content through auto-classification.
Recommendations
Hutton [0,1]-quasi-uniformities induced by fuzzy (quasi-)metric spaces
It is well known that given a probabilistic metric space (Menger space) with continuous t-norm T there is a Hausdorff topology associated. This association factorizes through strong uniformities (or (@e,@l)-uniformities). Similarly, any fuzzy metric ...
Completeness of Hutton [0,1]-quasi-uniform spaces
This paper deals with completeness of Hutton [0,1]-quasi-uniform spaces. Recently, the first two authors, [J. Gutierrez Garcia, M.A. de Prada Vicente, Hutton [0,1]-quasi-uniformities induced by fuzzy (quasi-)metric spaces, Fuzzy Sets and Systems 157 (...
Comments
Information & Contributors
Information
Published In
Elsevier B.V.
Publisher
Elsevier Science Publishers Ltd.
United Kingdom
Publication History
Published: 25 October 2023
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in