Cite

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Search in Google Scholar

[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Search in Google Scholar

[3] Haim Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, 2011.10.1007/978-0-387-70914-7Search in Google Scholar

[4] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Search in Google Scholar

[5] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Search in Google Scholar

[6] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Search in Google Scholar

[7] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Search in Google Scholar

[8] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Search in Google Scholar

[9] Noboru Endou, Yasunari Shidama, and Katsumasa Okamura. Baire’s category theorem and some spaces generated from real normed space. Formalized Mathematics, 14(4): 213-219, 2006. doi:10.2478/v10037-006-0024-x.10.2478/v10037-006-0024-xSearch in Google Scholar

[10] Krzysztof Hryniewiecki. Recursive definitions. Formalized Mathematics, 1(2):321-328, 1990.Search in Google Scholar

[11] Artur Korniłowicz. Recursive definitions. Part II. Formalized Mathematics, 12(2):167-172, 2004.Search in Google Scholar

[12] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1 (3):471-475, 1990.Search in Google Scholar

[13] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Search in Google Scholar

[14] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.Search in Google Scholar

[15] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.Search in Google Scholar

[16] Kazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Topological properties of real normed space. Formalized Mathematics, 22(3):209-223, 2014. doi:10.2478/forma-2014-0024.10.2478/forma-2014-0024Search in Google Scholar

[17] Keiko Narita, Noboru Endou, and Yasunari Shidama. Dual spaces and Hahn-Banach theorem. Formalized Mathematics, 22(1):69-77, 2014. doi:10.2478/forma-2014-0007.10.2478/forma-2014-0007Search in Google Scholar

[18] Keiko Narita, Noboru Endou, and Yasunari Shidama. Bidual spaces and reflexivity of real normed spaces. Formalized Mathematics, 22(4):303-311, 2014. doi:10.2478/forma-2014-0030.10.2478/forma-2014-0030Search in Google Scholar

[19] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.Search in Google Scholar

[20] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.Search in Google Scholar

[21] Bogdan Nowak and Andrzej Trybulec. Hahn-Banach theorem. Formalized Mathematics, 4(1):29-34, 1993.Search in Google Scholar

[22] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Search in Google Scholar

[23] Michael Reed and Barry Simon. Methods of modern mathematical physics. Vol. 1. Academic Press, New York, 1972.10.1016/B978-0-12-585001-8.50007-6Search in Google Scholar

[24] Walter Rudin. Functional Analysis. New York, McGraw-Hill, 2nd edition, 1991.Search in Google Scholar

[25] Hideki Sakurai, Hisayoshi Kunimune, and Yasunari Shidama. Uniform boundedness principle. Formalized Mathematics, 16(1):19-21, 2008. doi:10.2478/v10037-008-0003-5.10.2478/v10037-008-0003-5Search in Google Scholar

[26] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.Search in Google Scholar

[27] Yasumasa Suzuki, Noboru Endou, and Yasunari Shidama. Banach space of absolute summable real sequences. Formalized Mathematics, 11(4):377-380, 2003.Search in Google Scholar

[28] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.Search in Google Scholar

[29] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.Search in Google Scholar

[30] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Search in Google Scholar

[31] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Search in Google Scholar

[32] Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.Search in Google Scholar

[33] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Search in Google Scholar

[34] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Search in Google Scholar

[35] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Search in Google Scholar

[36] Kosaku Yoshida. Functional Analysis. Springer, 1980.Search in Google Scholar

[37] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Inferior limit and superior limit of sequences of real numbers. Formalized Mathematics, 13(3):375-381, 2005. Search in Google Scholar

eISSN:
1898-9934
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Computer Sciences, other, Mathematics, General Mathematics