UTILIZING SUPRA α-OPEN SETS TO

... In 1965, Njastad [13] presented and investigated a notion of α-open sets in topological spaces. Mildly compact (Mildly Lindelöf) spaces [15] were introduced in 1974 and almost compact spaces [9] were introduced in 1975 by Staum and Lambrinos, respectively. Mashhour et al.[11] introduced a concept o ...

... In 1965, Njastad [13] presented and investigated a notion of α-open sets in topological spaces. Mildly compact (Mildly Lindelöf) spaces [15] were introduced in 1974 and almost compact spaces [9] were introduced in 1975 by Staum and Lambrinos, respectively. Mashhour et al.[11] introduced a concept o ...

Supra b-compact and supra b

... Prof: We will show the case when A is supra b-compact relative to X, the other case is similar. Suppose that Ũ = {Uα : α ∈ ∆} is a cover of A ∩ B by supra b-open sets in X. Then Õ = {Uα : α ∈ ∆} ∪ {X − B} is a cover of A by supra b-open sets in X, but A is supra b-compact relative to X, so there e ...

... Prof: We will show the case when A is supra b-compact relative to X, the other case is similar. Suppose that Ũ = {Uα : α ∈ ∆} is a cover of A ∩ B by supra b-open sets in X. Then Õ = {Uα : α ∈ ∆} ∪ {X − B} is a cover of A by supra b-open sets in X, but A is supra b-compact relative to X, so there e ...

Topolog´ıa Algebraica de Espacios Topológicos Finitos y Aplicaciones

... between simple homotopy types of finite spaces and of simplicial complexes. This fundamental result allows us to study well-known geometrical problems from a new point of view, using all the combinatorial and topological machinery proper of finite spaces. Quillen’s conjecture on the poset of p-subgr ...

... between simple homotopy types of finite spaces and of simplicial complexes. This fundamental result allows us to study well-known geometrical problems from a new point of view, using all the combinatorial and topological machinery proper of finite spaces. Quillen’s conjecture on the poset of p-subgr ...

barmakthesis.pdf

... it seems that he was unaware of Stong’s and McCord’s results on finite spaces. We will see that the finite space point of view adds a completely new dimension to his conjecture and allows to attack the problem with new topological and combinatorial tools. We will show that Whitehead’s Theorem does ...

... it seems that he was unaware of Stong’s and McCord’s results on finite spaces. We will see that the finite space point of view adds a completely new dimension to his conjecture and allows to attack the problem with new topological and combinatorial tools. We will show that Whitehead’s Theorem does ...

About dual cube theorems

... the sense of Quillen [9]. Such categories (when pointed) have been shown to be the right place to build the theory of LS-category of their objects (spaces, simplicial sets, differential graded algebras, differential graded Lie algebras, etc.), provided an additional axiom holds: Axiom 2 in this pape ...

... the sense of Quillen [9]. Such categories (when pointed) have been shown to be the right place to build the theory of LS-category of their objects (spaces, simplicial sets, differential graded algebras, differential graded Lie algebras, etc.), provided an additional axiom holds: Axiom 2 in this pape ...

Homology stratifications and intersection homology Geometry & Topology Monographs Colin Rourke Brian Sanderson

... n–complex K and permutation π ∈ Σn+1 . Permutation homology is a convenient device (implicit in Goresky and MacPherson [2]) for studying intersection homology. We prove that, for a PL manifold, all permutation homology groups are the same as ordinary homology groups. In section 3 we prove that the g ...

... n–complex K and permutation π ∈ Σn+1 . Permutation homology is a convenient device (implicit in Goresky and MacPherson [2]) for studying intersection homology. We prove that, for a PL manifold, all permutation homology groups are the same as ordinary homology groups. In section 3 we prove that the g ...

PDF version - University of Warwick

... n–complex K and permutation π ∈ Σn+1 . Permutation homology is a convenient device (implicit in Goresky and MacPherson [2]) for studying intersection homology. We prove that, for a PL manifold, all permutation homology groups are the same as ordinary homology groups. In section 3 we prove that the g ...

... n–complex K and permutation π ∈ Σn+1 . Permutation homology is a convenient device (implicit in Goresky and MacPherson [2]) for studying intersection homology. We prove that, for a PL manifold, all permutation homology groups are the same as ordinary homology groups. In section 3 we prove that the g ...

On S-closed and Extremally Disconnected Fuzzy Topological Spaces

... The concept of lters in fuzzy set theory was introduced by Lowen and at the same time by Katsaras who studied in his work [11] fuzzy lters, ultra lters, clusters and the convergence of lters in fuzzy setting. In this paper we have developed the theory of lters a little further and introduced s- ...

... The concept of lters in fuzzy set theory was introduced by Lowen and at the same time by Katsaras who studied in his work [11] fuzzy lters, ultra lters, clusters and the convergence of lters in fuzzy setting. In this paper we have developed the theory of lters a little further and introduced s- ...

Introduction to Topological Groups

... internal description of the precompact groups using the notion of a big set of a group and we show that these are precisely the subgroups of the compact groups. Moreover, we define a precompact group G+ that “best approximates” G. Its completion bG, the Bohr compactification of G, is the compact gro ...

... internal description of the precompact groups using the notion of a big set of a group and we show that these are precisely the subgroups of the compact groups. Moreover, we define a precompact group G+ that “best approximates” G. Its completion bG, the Bohr compactification of G, is the compact gro ...

THE HOMOMORPHISMS OF TOPOLOGICAL GROUPOIDS 1

... The main purpose of this paper is to study topological groupoid homomorphisms and to give some kinds of special topological groupoid homomorphisms. Finally, some characterizations of these homomorphisms are given. AMS Mathematics Subject Classification (2010): 22A22, 20L05 Key words and phrases: Top ...

... The main purpose of this paper is to study topological groupoid homomorphisms and to give some kinds of special topological groupoid homomorphisms. Finally, some characterizations of these homomorphisms are given. AMS Mathematics Subject Classification (2010): 22A22, 20L05 Key words and phrases: Top ...

$\ alpha $-compact fuzzy topological spaces

... a-open cover of X has a finite subcover. D e f i n i t i o n 2.4. Let (X,T) and (Y, S) be fuzzy topological spaces. A mapping / : X -4 Y is called fuzzy a-continuous if the inverse image of each fuzzy open set in Y is fuzzy a-open in X. Definition 2 . 5 . A mapping / : X -> Y is said to be fuzzy a-i ...

... a-open cover of X has a finite subcover. D e f i n i t i o n 2.4. Let (X,T) and (Y, S) be fuzzy topological spaces. A mapping / : X -4 Y is called fuzzy a-continuous if the inverse image of each fuzzy open set in Y is fuzzy a-open in X. Definition 2 . 5 . A mapping / : X -> Y is said to be fuzzy a-i ...

Embeddings of compact convex sets and locally compact cones

... a natural way in the theory of compact semigroups [6]. ...

... a natural way in the theory of compact semigroups [6]. ...

PDF ( 40 )

... Proof. Let G be a mildly Ig -open set and int*(cl(G)) ⊆ H ⊆ G. Since int*(cl(G)) ⊆ H ⊆ G, then int*(cl(G)) = int*(cl(H)). Let K be a g-closed set and K ⊆ H. We have K ⊆ G. Since G is a mildly Ig -open set, it follows from Theorem 4.11 that K ⊆ int*(cl(G)) = int*(cl(H)). Hence, by Theorem 4.11, H is ...

... Proof. Let G be a mildly Ig -open set and int*(cl(G)) ⊆ H ⊆ G. Since int*(cl(G)) ⊆ H ⊆ G, then int*(cl(G)) = int*(cl(H)). Let K be a g-closed set and K ⊆ H. We have K ⊆ G. Since G is a mildly Ig -open set, it follows from Theorem 4.11 that K ⊆ int*(cl(G)) = int*(cl(H)). Hence, by Theorem 4.11, H is ...

THE SMOOTH IDEAL Introduction A measurable space is a set

... The desire to understand obstacles of definability inherent in mathematical classification problems recently led to the study of Borel cardinals associated with equivalence relations on standard Borel spaces. From this point forward, we will restrict our attention to such relations. As any two stand ...

... The desire to understand obstacles of definability inherent in mathematical classification problems recently led to the study of Borel cardinals associated with equivalence relations on standard Borel spaces. From this point forward, we will restrict our attention to such relations. As any two stand ...

An extension in fuzzy topological spaces

... that ÂA is the characteristic function of A, and the crisp topological space (X, [T ]) is called original topological space of (X; T ): De…nition 4 [13] A fuzzy topological space(X; T ) is called a week induction of the topological space (X; T0 ) if [T ] = T0 and each element of T is lower semi-cont ...

... that ÂA is the characteristic function of A, and the crisp topological space (X, [T ]) is called original topological space of (X; T ): De…nition 4 [13] A fuzzy topological space(X; T ) is called a week induction of the topological space (X; T0 ) if [T ] = T0 and each element of T is lower semi-cont ...

International Journal of Pure and Applied Mathematics

... to compact covering map studied by E. Michael [14, 15] and prove that a fuzzy continuous closed map from an induced fuzzy paracompact in to an arbitrary induced fuzzy topological space is fuzzy covering compact. We also define the fuzzy countable compact by using the finite open cover in the sense o ...

... to compact covering map studied by E. Michael [14, 15] and prove that a fuzzy continuous closed map from an induced fuzzy paracompact in to an arbitrary induced fuzzy topological space is fuzzy covering compact. We also define the fuzzy countable compact by using the finite open cover in the sense o ...

FIBRATIONS OF TOPOLOGICAL STACKS Contents 1. Introduction 2

... reader can consult [No2] and [No4] for more on paratopological stacks. 2. Review of homotopy theory of topological stacks In this section, we recall some basic facts and definitions from [No1] and [No2]. For a quick introduction to topological stacks the reader may also consult [No5]. Our terminolog ...

... reader can consult [No2] and [No4] for more on paratopological stacks. 2. Review of homotopy theory of topological stacks In this section, we recall some basic facts and definitions from [No1] and [No2]. For a quick introduction to topological stacks the reader may also consult [No5]. Our terminolog ...

On products of maximally resolvable spaces

... A maximally resolvable space is one which can be decomposed into the largest number of "maximally dense" subsets. Answering a previously posed question, we show that an arbitrary product of maximally resolvable spaces is again maximally resolvable, not only with respect to the ordinary product topol ...

... A maximally resolvable space is one which can be decomposed into the largest number of "maximally dense" subsets. Answering a previously posed question, we show that an arbitrary product of maximally resolvable spaces is again maximally resolvable, not only with respect to the ordinary product topol ...

Smooth Manifolds

... This book is about smooth manifolds. In the simplest terms, these are spaces that locally look like some Euclidean space Rn , and on which one can do calculus. The most familiar examples, aside from Euclidean spaces themselves, are smooth plane curves such as circles and parabolas, and smooth surfac ...

... This book is about smooth manifolds. In the simplest terms, these are spaces that locally look like some Euclidean space Rn , and on which one can do calculus. The most familiar examples, aside from Euclidean spaces themselves, are smooth plane curves such as circles and parabolas, and smooth surfac ...

A new definition of fuzzy compactness

... The following theorem is a generalization of the Alexander Subbase Theorem. Theorem 3.12. Let P (L) be order generating [4], R be a subbase for the L-topology T on a set X, and G ∈ LX . If for any a ∈ P (L), every strong a-shading (contained in R) of G has a ﬁnite subfamily V which is a strong a-sha ...

... The following theorem is a generalization of the Alexander Subbase Theorem. Theorem 3.12. Let P (L) be order generating [4], R be a subbase for the L-topology T on a set X, and G ∈ LX . If for any a ∈ P (L), every strong a-shading (contained in R) of G has a ﬁnite subfamily V which is a strong a-sha ...

Sir Michael Francis Atiyah, OM, FRS, FRSE, FMedSci FAA, HonFREng (born 22 April 1929) is a British mathematician specialising in geometry.Atiyah grew up in Sudan and Egypt and spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study. He has been president of the Royal Society (1990–1995), master of Trinity College, Cambridge (1990–1997), chancellor of the University of Leicester (1995–2005), and president of the Royal Society of Edinburgh (2005–2008). Since 1997, he has been an honorary professor at the University of Edinburgh.Atiyah's mathematical collaborators include Raoul Bott, Friedrich Hirzebruch and Isadore Singer, and his students include Graeme Segal, Nigel Hitchin and Simon Donaldson. Together with Hirzebruch, he laid the foundations for topological K-theory, an important tool in algebraic topology, which, informally speaking, describes ways in which spaces can be twisted. His best known result, the Atiyah–Singer index theorem, was proved with Singer in 1963 and is widely used in counting the number of independent solutions to differential equations. Some of his more recent work was inspired by theoretical physics, in particular instantons and monopoles, which are responsible for some subtle corrections in quantum field theory. He was awarded the Fields Medal in 1966, the Copley Medal in 1988, and the Abel Prize in 2004.