## Basis of Real Linear Space (1990)

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Citations: | 271 - 21 self |

### BibTeX

@MISC{Trybulec90basisof,

author = {Wojciech Trybulec},

title = {Basis of Real Linear Space},

year = {1990}

}

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### Abstract

this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G

### Citations

1297 | Functions and their basic properties
- Byliński
- 1990
(Show Context)
Citation Context ...linear space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], =-=[4]-=-, [5], [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a rea... |

1293 | Tarski Grothendieck set theory
- Trybulec
- 1990
(Show Context)
Citation Context ...by a set of vectors and basis of real linear space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles =-=[8]-=-, [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are s... |

1229 | Properties of subsets
- Trybulec
- 1990
(Show Context)
Citation Context ...f vectors and basis of real linear space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], =-=[16]-=-, [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b a... |

1049 | Functions from a set to a set
- Byliński
- 1990
(Show Context)
Citation Context ...r space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], =-=[5]-=-, [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real lin... |

1024 | Relations and their basic properties
- Woronowicz
- 1990
(Show Context)
Citation Context ...is of real linear space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], =-=[17]-=-, [2], [4], [5], [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, ... |

758 | Some basic properties of sets
- Byliński
- 1990
(Show Context)
Citation Context ...set of vectors and basis of real linear space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], =-=[6]-=-, [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, ... |

673 | The ordinal numbers
- Bancerek
- 1990
(Show Context)
Citation Context ...those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], [11], [15], and =-=[1]-=- provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, W1, W2, W3 are subspaces of V , v, v1,... |

660 | The fundamental properties of natural numbers
- Bancerek
- 1990
(Show Context)
Citation Context ...al linear space, operations on vectors: addition, multiplication by real number, inverse vector, subtraction. The sum of finite sequence of the vectors is also defined. Theorems that belong rather to =-=[1]-=- or [4] are proved. MML Identifier: RLVECT_1. WWW: http://mizar.org/JFM/Vol1/rlvect_1.html The articles [11], [8], [13], [2], [3], [12], [10], [14], [6], [7], [5], [9], [4], and [1] provide the notati... |

563 | Basic properties of real numbers
- Hryniewiecki
- 1990
(Show Context)
Citation Context .... Theorems that belong rather to [1] or [4] are proved. MML Identifier: RLVECT_1. WWW: http://mizar.org/JFM/Vol1/rlvect_1.html The articles [11], [8], [13], [2], [3], [12], [10], [14], [6], [7], [5], =-=[9]-=-, [4], and [1] provide the notation and terminology for this paper. We introduce loop structures which are extensions of zero structure and are systems 〈 a carrier, an addition, a zero 〉, where the ca... |

370 |
Subsets of real numbers
- Trybulec
(Show Context)
Citation Context ...ors and basis of real linear space are introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], =-=[10]-=-, [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are rea... |

352 | Binary operations
- Byliński
- 1990
(Show Context)
Citation Context ...fined. Theorems that belong rather to [1] or [4] are proved. MML Identifier: RLVECT_1. WWW: http://mizar.org/JFM/Vol1/rlvect_1.html The articles [11], [8], [13], [2], [3], [12], [10], [14], [6], [7], =-=[5]-=-, [9], [4], and [1] provide the notation and terminology for this paper. We introduce loop structures which are extensions of zero structure and are systems 〈 a carrier, an addition, a zero 〉, where t... |

330 | Finite sets
- Darmochwał
- 1990
(Show Context)
Citation Context ...oduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], =-=[7]-=-, [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, W1, W... |

307 | Domains and their Cartesian products
- Trybulec
- 1990
(Show Context)
Citation Context ...the vectors is also defined. Theorems that belong rather to [1] or [4] are proved. MML Identifier: RLVECT_1. WWW: http://mizar.org/JFM/Vol1/rlvect_1.html The articles [11], [8], [13], [2], [3], [12], =-=[10]-=-, [14], [6], [7], [5], [9], [4], and [1] provide the notation and terminology for this paper. We introduce loop structures which are extensions of zero structure and are systems 〈 a carrier, an additi... |

267 | Pigeon hole principle - Trybulec - 1990 |

208 | Finite sets - Darmochwal - 1990 |

164 | Partially ordered sets
- Trybulec
- 1990
(Show Context)
Citation Context ...e theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], =-=[12]-=-, [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, W1, W2, W3 are su... |

148 | Function domains and Frænkel operator
- Trybulec
- 1990
(Show Context)
Citation Context ... introduced. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], =-=[9]-=-, [7], [13], [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, ... |

37 | Subspaces and cosets of subspaces in real linear space
- Trybulec
- 1990
(Show Context)
Citation Context ...d. Some theorems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], =-=[13]-=-, [12], [11], [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, W1, W2, W3 ... |

31 | Linear combinations in real linear space
- Trybulec
- 1990
(Show Context)
Citation Context ...oncerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], [11], =-=[15]-=-, and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, W1, W2, W3 are subspaces of V... |

22 | Function domains and Fraenkel operator - Trybulec - 1990 |

8 | Operations on subspaces in real linear space
- Trybulec
- 1989
(Show Context)
Citation Context ...rems concerning those notions are proved. MML Identifier:RLVECT_3. WWW:http://mizar.org/JFM/Vol2/rlvect_3.html The articles [8], [6], [16], [10], [3], [17], [2], [4], [5], [14], [9], [7], [13], [12], =-=[11]-=-, [15], and [1] provide the notation and terminology for this paper. For simplicity, we follow the rules: x, X, Y , Z are sets, a, b are real numbers, V is a real linear space, W1, W2, W3 are subspace... |