Kuratowski closure axioms (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kuratowski closure axioms" in English language version.

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Monteiro (1945), p. 160. Monteiro, António (1945), "Caractérisation de l'opération de fermeture par un seul axiome" [Characterization of the operation of closure by a single axiom], Portugaliae mathematica (in French), vol. 4, no. 4, pp. 158–160, MR 0012310, Zbl 0060.39406.
Monteiro (1945), p. 158. Monteiro, António (1945), "Caractérisation de l'opération de fermeture par un seul axiome" [Characterization of the operation of closure by a single axiom], Portugaliae mathematica (in French), vol. 4, no. 4, pp. 158–160, MR 0012310, Zbl 0060.39406.

icm.edu.pl

matwbn.icm.edu.pl

Kuratowski (1922). Kuratowski, Kazimierz (1922) [1920], "Sur l'opération A de l'Analysis Situs" [On the operation A in Analysis Situs] (PDF), Fundamenta Mathematicae (in French), vol. 3, pp. 182–199.

loc.gov

lccn.loc.gov

Pervin (1964), p. 44. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
Pervin (1964), p. 43, Exercise 6. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
Kuratowski (1966), p. 38. Kuratowski, Kazimierz (1966) [1958], Topology, vol. I, translated by Jaworowski, J., Academic Press, ISBN 0-12-429201-1, LCCN 66029221.
- Arkhangel'skij & Fedorchuk (1990), p. 25. Arkhangel'skij, A.V.; Fedorchuk, V.V. (1990) [1988], Gamkrelidze, R.V.; Arkhangel'skij, A.V.; Pontryagin, L.S. (eds.), General Topology I, Encyclopaedia of Mathematical Sciences, vol. 17, translated by O'Shea, D.B., Berlin: Springer-Verlag, ISBN 978-3-642-64767-3, LCCN 89-26209.
- Pervin (1964), p. 42, Exercise 5. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 46, Exercise 4. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Arkhangel'skij & Fedorchuk (1990), p. 26. Arkhangel'skij, A.V.; Fedorchuk, V.V. (1990) [1988], Gamkrelidze, R.V.; Arkhangel'skij, A.V.; Pontryagin, L.S. (eds.), General Topology I, Encyclopaedia of Mathematical Sciences, vol. 17, translated by O'Shea, D.B., Berlin: Springer-Verlag, ISBN 978-3-642-64767-3, LCCN 89-26209.
- Pervin (1964), p. 43, Exercise 10. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 49, Theorem 3.4.3. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 60, Theorem 4.3.1. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 66, Exercise 3. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 67, Exercise 5. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 69, Theorem 5.1.1. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 70, Theorem 5.1.2. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), pp. 193–196. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.
- Pervin (1964), p. 51. Pervin, William J. (1964), Boas, Ralph P. Jr. (ed.), Foundations of General Topology, Academic Press, ISBN 9781483225159, LCCN 64-17796.

ncatlab.org

"Moore closure". nLab. March 7, 2015. Retrieved August 19, 2019.

purl.pt

Monteiro (1945), p. 160. Monteiro, António (1945), "Caractérisation de l'opération de fermeture par un seul axiome" [Characterization of the operation of closure by a single axiom], Portugaliae mathematica (in French), vol. 4, no. 4, pp. 158–160, MR 0012310, Zbl 0060.39406.
Monteiro (1945), p. 158. Monteiro, António (1945), "Caractérisation de l'opération de fermeture par un seul axiome" [Characterization of the operation of closure by a single axiom], Portugaliae mathematica (in French), vol. 4, no. 4, pp. 158–160, MR 0012310, Zbl 0060.39406.

researchgate.net

Kuratowski (1966), p. 38. Kuratowski, Kazimierz (1966) [1958], Topology, vol. I, translated by Jaworowski, J., Academic Press, ISBN 0-12-429201-1, LCCN 66029221.

stackexchange.com

math.stackexchange.com

A proof for the case $\lambda =\aleph _{0}$ can be found at "Is the following a Kuratowski closure operator?!". Stack Exchange. November 21, 2015.
A proof can be found at this link.

zbmath.org

Monteiro (1945), p. 160. Monteiro, António (1945), "Caractérisation de l'opération de fermeture par un seul axiome" [Characterization of the operation of closure by a single axiom], Portugaliae mathematica (in French), vol. 4, no. 4, pp. 158–160, MR 0012310, Zbl 0060.39406.
Monteiro (1945), p. 158. Monteiro, António (1945), "Caractérisation de l'opération de fermeture par un seul axiome" [Characterization of the operation of closure by a single axiom], Portugaliae mathematica (in French), vol. 4, no. 4, pp. 158–160, MR 0012310, Zbl 0060.39406.