Artur Korniłowicz -- Mizar Articles

2017

  1. Simple-named complex-valued nominative data -- definition and basic operations, Formalized Mathematics, 25(3):205--216, 2017. (with Ievgen Ivanov, Mykola Nikitchenko and Andrii Kryvolap)
  2. Basel problem, Formalized Mathematics, 25(2):149--155, 2017. (with Karol Pak)
  3. Basel problem -- preliminaries, Formalized Mathematics, 25(2):141--147, 2017. (with Karol Pak)
  4. Vieta's formula about the sum of roots of polynomials, Formalized Mathematics, 25(2):87--92, 2017. (with Karol Pak)
  5. All Liouville Numbers are Transcendental, Formalized Mathematics, 25(1):49--54, 2017. (with Adam Naumowicz and Adam Grabowski)
  6. Introduction to Liouville Numbers, Formalized Mathematics, 25(1):39--48, 2017. (with Adam Grabowski)
  7. Differentiability of Polynomials over Reals, Formalized Mathematics, 25(1):31--37, 2017.
2016
  1. Niven's Theorem, Formalized Mathematics, 24(4):301--308, 2016. (with Adam Naumowicz)
  2. Some Algebraic Properties of Polynomial Rings, Formalized Mathematics, 24(3):227--237, 2016. (with Christoph Schwarzweller)
2015
  1. Characteristic of Rings. Prime Fields, Formalized Mathematics, 23(4):333--349, 2015. (with Christoph Schwarzweller)
2014
  1. The First Isomorphism Theorem and Other Properties of Rings, Formalized Mathematics, 22(4):291--301, 2014. (with Christoph Schwarzweller)
  2. Pseudo-Canonical Formulae are Classical, Formalized Mathematics, 22(2):99--103, 2014. (with Marco B. Caminati)
2013
  1. Coproducts in Categories without Uniqueness of cod and dom, Formalized Mathematics, 21(4):235--239, 2013. (with Maciej Golinski)
  2. Commutativeness of Fundamental Groups of Topological Groups, Formalized Mathematics, 21(2):127--131, 2013.
2012
  1. Products in Categories without Uniqueness of cod and dom, Formalized Mathematics, 20(4):303--307, 2012.
  2. Contracting Mapping on Normed Linear Space, Formalized Mathematics, 20(4):291--301, 2012. (with Keiichi Miyajima and Yasunari Shidama)
  3. Cayley-Dickson Construction, Formalized Mathematics, 20(4):281--290, 2012.
  4. The Borsuk-Ulam Theorem, Formalized Mathematics, 20(2):105--112, 2012. (with Marco Riccardi)
  5. Fundamental Group of n-sphere for n >= 2, Formalized Mathematics, 20(2):97--104, 2012. (with Marco Riccardi)
  6. Riemann Integral of Functions from R into n-dimensional Real Normed Space, Formalized Mathematics, 20(1):79--86, 2012. (with Keiichi Miyajima and Yasunari Shidama)
  7. The Differentiable Functions from R into R^n , Formalized Mathematics, 20(1):65--71, 2012. (with Keiko Narita and Yasunari Shidama)
  8. Valuation Theory, Part I, Formalized Mathematics, 20(1):7--14, 2012. (with Grzegorz Bancerek and Hidetsune Kobayashi)
2011
  1. More on the Continuity of Real Functions, Formalized Mathematics, 19(4):233--239, 2011. (with Keiko Narita and Yasunari Shidama)
  2. Cayley's Theorem, Formalized Mathematics, 19(4):223--225, 2011.
  3. Mazur-Ulam Theorem, Formalized Mathematics, 19(3):127--130, 2011.
2010
  1. On the Continuity of Some Functions, Formalized Mathematics, 18(3):175--183, 2010.
  2. Miscellaneous Facts about Open Functions and Continuous Functions, Formalized Mathematics, 18(3):171--174, 2010.
  3. The Correspondence Between n-dimensional Euclidean Space and the Product of n Real Lines, Formalized Mathematics, 18(1):81--85, 2010.
2009
  1. Collective Operations on Number-Membered Sets, Formalized Mathematics, 17(2):99--115, 2009.
  2. Arithmetic Operations on Functions from Sets into Functional Sets, Formalized Mathematics, 17(1):43--60, 2009.
  3. The Real Vector Spaces of Finite Sequences Are Finite Dimensional, Formalized Mathematics, 17(1):1--9, 2009. (with Yatsuka Nakamura, Nagato Oya and Yasunari Shidama)
2007
  1. Basic Operations on Preordered Coherent Spaces, Formalized Mathematics, 15(4):213--230, 2007. (with Klaus E. Grue)
2006
  1. Simple Continued Fractions and Their Convergents, Formalized Mathematics, 14(3):71--78, 2006. (with Bo Li and Yan Zhang)
2005
  1. Quotient Rings, Formalized Mathematics, 13(4):573--576, 2005.
  2. Jordan Curve Theorem, Formalized Mathematics, 13(4):481--491, 2005.
  3. Tietze Extension Theorem, Formalized Mathematics, 13(4):471--475, 2005. (with Grzegorz Bancerek and Adam Naumowicz)
  4. The Fashoda Meet Theorem for Continuous Mappings, Formalized Mathematics, 13(4):467--469, 2005. (with Yatsuka Nakamura and Andrzej Trybulec)
  5. Brouwer Fixed Point Theorem for Disks on the Plane, Formalized Mathematics, 13(2):333--336, 2005. (with Yasunari Shidama)
  6. The Fundamental Group of the Circle, Formalized Mathematics, 13(2):325--331, 2005.
  7. Properties of Connected Subsets of the Real Line, Formalized Mathematics, 13(2):315--323, 2005.
  8. On the Real Valued Functions, Formalized Mathematics, 13(1):181--187, 2005.
  9. Some Properties of Circles on the Plane, Formalized Mathematics, 13(1):117--124, 2005. (with Yasunari Shidama)
  10. Some Properties of Rectangles on the Plane, Formalized Mathematics, 13(1):109--115, 2005. (with Yasunari Shidama)
  11. On Some Points of a Simple Closed Curve. Part II, Formalized Mathematics, 13(1):89--91, 2005. (with Adam Grabowski)
  12. On Some Points of a Simple Closed Curve, Formalized Mathematics, 13(1):81--87, 2005.
  13. Inverse Trigonometric Functions Arcsin and Arccos, Formalized Mathematics, 13(1):73--79, 2005. (with Yasunari Shidama)
2004
  1. On the Fundamental Groups of Products of Topological Spaces, Formalized Mathematics, 12(3):421--425, 2004.
  2. On the Isomorphism of Fundamental Groups, Formalized Mathematics, 12(3):391--396, 2004.
  3. Intersections of Intervals and Balls in TOP-REAL n, Formalized Mathematics, 12(3):301--306, 2004. (with Yasunari Shidama)
  4. The Fundamental Group of Convex Subspaces of TOP-REAL n, Formalized Mathematics, 12(3):295--299, 2004.
  5. The Uniform Continuity of Functions on Normed Linear Spaces, Formalized Mathematics, 12(3):277--279, 2004. (with Takaya Nishiyama and Yasunari Shidama)
  6. The Fundamental Group, Formalized Mathematics, 12(3):261--268, 2004. (with Yasunari Shidama and Adam Grabowski)
  7. Algebraic Properties of Homotopies, Formalized Mathematics, 12(3):251--260, 2004. (with Adam Grabowski)
  8. Fundamental Theorem of Arithmetic, Formalized Mathematics, 12(2):179--185, 2004. (with Piotr Rudnicki)
  9. Recursive Definitions. Part II, Formalized Mathematics, 12(2):167--172, 2004.
  10. Relocability for SCM over Ring, Formalized Mathematics, 12(2):151--157, 2004. (with Yasunari Shidama)
  11. A Tree of Execution of a Macroinstruction, Formalized Mathematics, 12(1):33--37, 2004.
2003
  1. SCMPDS Is Not Standard, Formalized Mathematics, 11(4):421--424, 2003. (with Yasunari Shidama)
  2. Morphism Into Chains. Part I, Formalized Mathematics, 11(2):189--195, 2003.
2002
  1. The Ordering of Points on a Curve, Part IV, Formalized Mathematics, 10(3):173--177, 2002.
  2. The Ordering of Points on a Curve, Part III, Formalized Mathematics, 10(3):169--171, 2002.
2001
  1. Yet Another Construction of Free Algebra, Formalized Mathematics, 9(4):779--785, 2001. (with Grzegorz Bancerek)
  2. On the Instructions of SCM+FSA, Formalized Mathematics, 9(4):673--679, 2001.
  3. Input and Output of Instructions, Formalized Mathematics, 9(4):665--671, 2001.
  4. On the Instructions of SCM, Formalized Mathematics, 9(4):659--663, 2001.
  5. Gauges and Cages. Part II, Formalized Mathematics, 9(3):555--558, 2001. (with Robert Milewski)
  6. Some Properties of Cells and Gauges, Formalized Mathematics, 9(3):545--548, 2001. (with Andrzej Trybulec and Adam Grabowski)
  7. Some Properties of Cells and Arcs, Formalized Mathematics, 9(3):531--535, 2001. (with Andrzej Trybulec, Robert Milewski and Adam Naumowicz)
  8. Gauges and Cages. Part I, Formalized Mathematics, 9(3):501--509, 2001. (with Andrzej Trybulec, Robert Milewski and Adam Naumowicz)
  9. The Properties of Instructions of SCM over Ring, Formalized Mathematics, 9(2):317--322, 2001.
  10. On the Composition of Macro Instructions of Standard Computers, Formalized Mathematics, 9(2):303--316, 2001.
  11. Standard Ordering of Instruction Locations, Formalized Mathematics, 9(2):291--301, 2001. (with Andrzej Trybulec and Piotr Rudnicki)
  12. Meet Continuous Lattices Revisited, Formalized Mathematics, 9(2):249--254, 2001.
  13. Injective Spaces. Part II, Formalized Mathematics, 9(1):41--47, 2001. (with Jarosław Gryko)
  14. Properties of the External Approximation of Jordan's Curve, Formalized Mathematics, 9(1):31--34, 2001.
  15. Some Properties of Isomorphism between Relational Structures. On the Product of Topological Spaces, Formalized Mathematics, 9(1):13--18, 2001. (with Jarosław Gryko)
1999
  1. Properties of Left-, and Right Components, Formalized Mathematics, 8(1):163--168, 1999.
  2. The Definition of Riemann Definite Integral and some Related Lemmas, Formalized Mathematics, 8(1):93--102, 1999. (with Noboru Endou)
  3. Homeomorphism between [:TOP-REAL i,TOP-REAL j:] and TOP-REAL (i+j), Formalized Mathematics, 8(1):73--76, 1999.
  4. Compactness of the Bounded Closed Subsets of TOP-REAL 2, Formalized Mathematics, 8(1):61--68, 1999.
1998
  1. The Basic Properties of \bf SCM over Ring, Formalized Mathematics, 7(2):301--305, 1998.
  2. The Construction of \bf SCM over Ring, Formalized Mathematics, 7(2):295--300, 1998.
  3. Introduction to Meet-Continuous Topological Lattices, Formalized Mathematics, 7(2):279--283, 1998.
  4. The Definition and Basic Properties of Topological Groups, Formalized Mathematics, 7(2):217--225, 1998.
  5. The Product of the Families of the Groups, Formalized Mathematics, 7(1):127--134, 1998.
  6. On the Characterization of Hausdorff Spaces, Formalized Mathematics, 7(1):63--68, 1998.
  7. The Properties of Product of Relational Structures, Formalized Mathematics, 7(1):45--52, 1998.
  8. The Composition of Functors and Transformations in Alternative Categories, Formalized Mathematics, 7(1):1--7, 1998.
1997
  1. On the Categories Without Uniqueness of cod and dom. Some Properties of the Morphisms and the Functors, Formalized Mathematics, 6(4):475--481, 1997.
  2. Convergence and the Limit of Complex Sequences. Serieses, Formalized Mathematics, 6(3):403--410, 1997. (with Yasunari Shidama)
  3. Birkhoff Theorem for Many Sorted Algebras, Formalized Mathematics, 6(3):389--395, 1997.
  4. Equations in Many Sorted Algebras, Formalized Mathematics, 6(3):363--369, 1997.
  5. On the Baire Category Theorem, Formalized Mathematics, 6(2):321--327, 1997.
  6. On the Topological Properties of Meet-Continuous Lattices, Formalized Mathematics, 6(2):269--277, 1997.
  7. Meet-Continuous Lattices, Formalized Mathematics, 6(1):159--167, 1997.
  8. Definitions and Properties of the Join and Meet of Subsets, Formalized Mathematics, 6(1):153--158, 1997.
  9. Cartesian Products of Relations and Relational Structures, Formalized Mathematics, 6(1):145--152, 1997.
  10. On the Trivial Many Sorted Algebras and Many Sorted Congruences, Formalized Mathematics, 6(1):9--15, 1997.
1996
  1. On the Closure Operator and the Closure System of Many Sorted Sets, Formalized Mathematics, 5(4):543--551, 1996.
  2. On the Many Sorted Closure Operator and the Many Sorted Closure System, Formalized Mathematics, 5(4):529--536, 1996.
  3. Certain Facts about Families of Subsets of Many Sorted Sets, Formalized Mathematics, 5(3):451--456, 1996.
  4. Some Basic Properties of Many Sorted Sets, Formalized Mathematics, 5(3):395--399, 1996.
  5. Definitions and Basic Properties of Boolean and Union of Many Sorted Sets, Formalized Mathematics, 5(2):279--281, 1996.
  6. Extensions of Mappings on Generator Set, Formalized Mathematics, 5(2):269--272, 1996.
  7. On the Group of Automorphisms of Universal Algebra and Many Sorted Algebra, Formalized Mathematics, 5(2):221--226, 1996.
  8. On the Group of Inner Automorphisms, Formalized Mathematics, 5(1):43--45, 1996.

May 31, 2017 --- arturk@math.uwb.edu.pl