scholarly journals Classification of separately continuous mappings with values in o-metrizable spaces

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Olena Karlova
Keyword(s):  
Continuous Mappings ◽  
Metrizable Spaces

Homotopy invariants and continuous mappings

1950 ◽  
Vol 202 (1069) ◽  
pp. 253-263 ◽  
Keyword(s):  
Homotopy Type ◽  
Betti Numbers ◽  
Continuous Mappings ◽  
Numerical Invariants ◽  
Homotopy Invariants

This paper contributes new numerical invariants to the topology of a certain class of polyhedra. These invariants, together with the Betti numbers and coefficients of torsion, characterize the homotopy type of one of these polyhedra. They are also applied to the classification of continuous mappings of an ( n + 2)-dimensional polyhedron into an ( n + 1)-sphere ( n > 2).

Separating Closed Sets by Continuous Mappings into Developable Spaces

1981 ◽  
Vol 33 (6) ◽  
pp. 1420-1431 ◽  
Author(s):  
Harald Brandenburg
Keyword(s):  
Topological Space ◽  
Double Sequence ◽  
Completely Regular ◽  
Closed Sets ◽  
Continuous Mappings ◽  
Neighbourhood Base ◽  
Image Position ◽  
Metrizable Spaces ◽  
Metrization Theorem ◽  
Developable Spaces

A topological space X is called developable if it has a development, i.e., a sequence of open covers of X such that for each x ∈ X the collection is a neighbourhood base of x, whereThis class of spaces has turned out to be one of the most natural and useful generalizations of metrizable spaces [23]. In [4] it was shown that some well known results in metrization theory have counterparts in the theory of developable spaces (i.e., Urysohn's metrization theorem, the Nagata-Smirnov theorem, and Nagata's “double sequence theorem”). Moreover, in [3] it was pointed out that subspaces of products of developable spaces (i.e., D-completely regular spaces) can be characterized in much the same way as subspaces of products of metrizable spaces (i.e., completely regular T1-spaces).

Injectivity of the Connecting Maps in AH Inductive Limit Systems

2005 ◽  
Vol 48 (1) ◽  
pp. 50-68 ◽  
Author(s):  
George A. Elliott ◽  
Guihua Gong ◽  
Liangqing Li
Keyword(s):  
Simplicial Complex ◽  
Inductive Limit ◽  
Extra Condition ◽  
The Third ◽  
Finite Simplicial Complex ◽  
Image Position ◽  
Metrizable Spaces ◽  
Special Case

AbstractLet A be the inductive limit of a systemwith , where Xn,i is a finite simplicial complex, and Pn,i is a projection in M[n,i](C(Xn,i)). In this paper, we will prove that A can be written as another inductive limitwith , where Yn,i is a finite simplicial complex, and Qn, i is a projection inM{n,i}(C(Yn,i)), with the extra condition that all the maps ψn,n+1 are injective. (The result is trivial if one allows the spaces Yn,i to be arbitrary compact metrizable spaces.) This result is important for the classification of simple AH algebras. The special case that the spaces Xn,iare graphs is due to the third author.

Homotopy classification of a class of continuous mappings

1982 ◽  
Vol 31 (5) ◽  
pp. 404-410 ◽  
Author(s):  
V. T. Dmitrienko ◽  
V. G. Zvyagin
Keyword(s):  
Homotopy Classification ◽  
Continuous Mappings

scholarly journals On a Homotopy Classification of Mappings of an (n+1) Dimensional Complex Into an Arcwise Connected Topological Space Which is Aspherical in Dimensions Less Thann (n >2)

1951 ◽  
Vol 3 ◽  
pp. 67-72 ◽  
Author(s):  
Nobuo Shimada ◽  
Hiroshi Uehara
Keyword(s):  
Topological Space ◽  
Nauk Sssr ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Homotopy Classification ◽  
Homotopy Classes ◽  
Continuous Mappings ◽  
Arcwise Connected ◽  
New Type

Pontrjagin classified mappings of a three dimensional sphere into anndimensional complex, where he made use of a new type of product of cocycles. By the aid of the generalized Pontrjagin’s product of cocycles Steenrod enumerated effectively all the homotopy classes of mappings of an (n+1) dimensional complex into annsphere. According to the recent issue of the Mathematical Reviews it is reported that M. M. Postnikov extended Steenrod’s case to the case where an arcwise connected topological space which is aspherical in dimensions less thann, takes place of annsphere. (Postnikov M. M., Classification of continuous mappings of an(n+1)dimensional complex into a connected topological space which is aspherical in dimensions less thann. Doklady Akad. Nauk SSSR (N.S.) 71., 1027-1028, 1950 (Russian. No. proof is given.)) But here in Japan no details are yet to hand. We intend to give a solution to this problem in case wheren>2, and also to give an application concerning the(n+ 3)-extension cocycle.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

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