Abstract
Y. Imai, K. Iseki [4], and K. Iseki [5] presented types from summary algebras which are called BCK-algebras and BCI-algebras. It is known that the brand of BCK algebras is a suitable subtype from the type from BCI-algebras. The researchers Q. P. Hu [2] & X. Li [3] presented a width type from essence algebras: BCH- algebras. They have exhibited that the type of BCI-algebras is a suitable subtype of the type of BCH-algebras. Moreover, J. Neggers and H. S. K [9] presented the connotation from d - algebras that are else popularization from BCK-algebras, inspected kinsmen amidst d-algebras & BCK-algebras. They calculated diversified topologies to research from lattices but they did not discuss the experience of making the binary operation of d- algebra continuous. Topological set notions are famous and yet accurate by numerous mathematicians. Even global topographical algebraic structure is sought by several writers. We realize a Tb-algebra, get it several ownerships of such build, the generality significant flavors and arrive to realize a new gender of spaces designated BP- space, where we arrived the results. Let <img src=image/13425357_01.gif> be <img src=image/13425357_02.gif> B-space and <img src=image/13425357_03.gif> is periodic proportional. Then <img src=image/13425357_04.gif> is a compact set in <img src=image/13425357_01.gif> and <img src=image/13425357_04.gif> = <img src=image/13425357_05.gif>, <img src=image/13425357_06.gif>. Also If <img src=image/13425357_07.gif> is an invariant under <img src=image/13425357_08.gif>, then <img src=image/13425357_09.gif>, <img src=image/13425357_10.gif> and <img src=image/13425357_11.gif> are invariant under <img src=image/13425357_12.gif> for every Q in <img src=image/13425357_13.gif> if <img src=image/13425357_14.gif> is also. If the function <img src=image/13425357_14.gif> is closed (one to one) then <img src=image/13425357_15.gif>, (<img src=image/13425357_16.gif>) is invariant under <img src=image/13425357_12.gif> and the set of interior points of <img src=image/13425357_18.gif> is invariant under <img src=image/13425357_12.gif>, if the function <img src=image/13425357_14.gif> is open and <img src=image/13425357_17.gif>.
Highlights
K [9] presented the connotation from d - algebras that are else popularization from BCK-algebras, inspected kinsmen amidst d-algebras & BCK-algebras. They calculated diversified topologies to research from lattices but they did not discuss the experience of making the binary operation of d- algebra continuous
Even global topographical algebraic structure is sought by several writers
We have begun the lesson of topological b-algebra in this paper, so we want some preliminary indispensable to amplify the paper and contain some of the outcrops of the basic knowledge of algebra b which is a prerequisite for lessoning this topic
Summary
We have begun the lesson of topological b-algebra in this paper, so we want some preliminary indispensable to amplify the paper and contain some of the outcrops of the basic knowledge of algebra b which is a prerequisite for lessoning this topic.
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