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...s that are necessary in the proof have been proved. MML Identifier: BORSUK_1. WWW: http://mizar.org/JFM/Vol3/borsuk_1.html The articles [20], [8], [22], [11], [23], [5], [21], [19], [17], [13], [12], =-=[3]-=-, [7], [16], [6], [15], [24], [10], [9], [14], [4], and [18] provide the notation and terminology for this paper. 1. PRELIMINARIES We use the following convention: e, u, X, Y , X1, X2, Y1, Y2 are sets...

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...rs, several projects have aimed at providing computer assistance for doing mathematics. Among the better known there are: AUTOMATH [4], EKL [10], QUIP [22], Nuprl [3], THEAX [14], Computational Logic =-=[2]-=-, Ontic [11], and the more recent ones such as ALF, ELF, HOL, LEGO and many others (see [6, 7]). The specic goals of these projects vary. However, they have one common feature: the human writes mathe...

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...orems concerning sequences are proved. MML Identifier: METRIC_6. WWW: http://mizar.org/JFM/Vol3/metric_6.html The articles [15], [5], [17], [1], [16], [12], [18], [3], [4], [7], [8], [11], [9], [10], =-=[2]-=-, [6], [13], and [14] provide the notation and terminology for this paper. For simplicity, we follow the rules: X is a metric space, x, y, z are elements of X, A is a non empty set, a is an element of...

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...ox. MML Identifier:PSCOMP_1. WWW:http://mizar.org/JFM/Vol9/pscomp_1.html The articles [20], [23], [1], [22], [16], [7], [18], [10], [21], [24], [3], [4], [13], [12], [15], [11], [19], [17], [6], [5], =-=[2]-=-, [8], and [9] provide the notation and terminology for this paper. 1. PRELIMINARIES Let X be a set. Let us observe that X has non empty elements if and only if: (Def. 1) 0 /∈ X. We introduce X is wit...

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...ed to prove reflexivity and symmetry of the above predicate. MML Identifier:BORSUK_2. WWW:http://mizar.org/JFM/Vol9/borsuk_2.html The articles [20], [10], [22], [16], [23], [7], [9], [8], [19], [13], =-=[4]-=-, [1], [12], [18], [11], [17], [21], [24], [14], [6], [5], [2], and [3] provide the notation and terminology for this paper. 1. PRELIMINARIES In this paper T , T1, T2, S are non empty topological spac...

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... and hereditarily extremally disconnected topological spaces (comp. [9], [6]). MML Identifier:TDLAT_3. WWW:http://mizar.org/JFM/Vol4/tdlat_3.html The articles [14], [5], [16], [11], [18], [12], [19], =-=[3]-=-, [15], [4], [20], [1], [17], and [8] provide the notation and terminology for this paper. 1. SELECTED PROPERTIES OF SUBSETS OF A TOPOLOGICAL SPACE In this paper X is a topological space and C is a su...

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...e boundary of any rectangle inE 2 T is open and connected. MML Identifier:JORDAN1. WWW:http://mizar.org/JFM/Vol4/jordan1.html The articles [14], [16], [1], [9], [17], [4], [5], [3], [12], [11], [10], =-=[2]-=-, [15], [7], and [6] provide the notation and terminology for this paper. 1. SELECTED THEOREMS ON CONNECTED SPACES In this paper G1, G2 are non empty topological spaces and x, y are points of G1. One ...