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9. Maths IJMCAR SEMI CONNECTEDNESS AND PRE CONNECTEDNESS Bhagyashri |
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A ech closure space (X, u) is a set X with ech closure |
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operator u: P(X) P(X) which satisfies u , A uA for every |
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A X, u (A B) = uA uB, for all A, B X. Many properties |
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which hold in topological space hold in closure space as |
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well. The notion of connectedness that is familiar from |
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topological space generalized to closure space. A subset A |
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of a topological space (X, ) is called semi-open if A cl |
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(int (A)) and pre-open if A int (cl (A)), where cl is a |
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closure function in topological space. We further extend |
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the notion of semi-open set and pre-open set in closure |
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space. The aim of this paper is to introduce and study |
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the concept of semi-connectedness and pre-connectedness |
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in closure 1space using the notion of semi-open set and |
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pre-open set of closure space. |
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Date Published: 2014-11-01 11:48:44 |
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Identifier: 9.MathsIJMCARSEMICONNECTEDNESSANDPRECONNECTEDNESSBhagyashri |
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Item Size: 3417425 |
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Language: English |
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Media Type: texts |
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# Topics |
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Closure Space |
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Connected Space |
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Connected Closure Space |
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Semi-Open Sets |
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Pre-Open Sets |
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Semi-Continuous Function |
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Pre-Continuous Function |
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Semi-Connected Closure Space |
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Pre-Connected Closure Space |
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