scholarly journals Weak Forms of Continuity andcmd="newline"Associated Properties

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Mohammad S. Sarsak
Keyword(s):  
Continuous Mapping ◽  
Open Mapping ◽  
Almost Open

We introduce slightly -continuous mapping and almost -open mapping and investigate the relationships between these mappings and related types of mappings, and also study some properties of these mappings.

scholarly journals On FuzzySp-Open Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Hakeem A. Othman
Keyword(s):  
Topological Space ◽  
Continuous Mapping ◽  
Open Mapping ◽  
New Class ◽  
Fuzzy Topological Space ◽  
The Relationship

A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzysp-open sets, are introduced, and their properties are studied and the relationship between this new concept and other weaker forms of fuzzy open sets we discussed. Moreover, we introduce the fuzzysp-continuous (resp., fuzzysp-open) mapping and other stronger forms ofsp-continuous (resp., fuzzysp-open) mapping and establish their various characteristic properties. Finally, we study the relationships between all these mappings and other weaker forms of fuzzy continuous mapping and introduce fuzzysp-connected. Counter examples are given to show the noncoincidence of these sets and mappings.

scholarly journals On the inverse image of Baire spaces

1997 ◽  
Vol 20 (3) ◽  
pp. 423-432
Author(s):  
Mustafa Çiçek
Keyword(s):  
Continuous Mapping ◽  
Inverse Image ◽  
Baire Space ◽  
Open Mapping ◽  
Separable Space

In 1961, Z. Frolik proved that iffis an open and continuous mapping of a metrizable separable spaceXonto Baire spaceYand if the point inverses are Baire spaces, thenXis a Baire space. We give a generalization to semi-continuous and semi-open mapping of this theorem and extended it to the several types of mappings.

Cerebellopontine Angle Surgery Assisted by Continuous Mapping of the Facial Nerve Via the Ultrasonic Aspirator

2020 ◽  
Author(s):  
Marco Cenzato ◽  
Roberto Stefini ◽  
Francesco Zenga ◽  
Maurizio Piparo ◽  
Alberto Debernardi ◽  
...  
Keyword(s):  
Electrical Stimulation ◽  
Facial Nerve ◽  
Cerebellopontine Angle ◽  
Continuous Mapping ◽  
Cost Effective ◽  
Current Intensity ◽  
Vestibular Schwannomas ◽  
Constant Current ◽  
Surgical Workflow ◽  
Ultrasonic Aspirator

Abstract Background Cerebellopontine angle (CPA) surgery carries the risk of lesioning the facial nerve. The goal of preserving the integrity of the facial nerve is usually pursued with intermittent electrical stimulation using a handheld probe that is alternated with the resection. We report our experience with continuous electrical stimulation delivered via the ultrasonic aspirator (UA) used for the resection of a series of vestibular schwannomas. Methods A total of 17 patients with vestibular schwannomas, operated on between 2010 and 2018, were included in this study. A constant-current stimulator was coupled to the UA used for the resection, delivering square-wave pulses throughout the resection. The muscle responses from upper and lower face muscles triggered by the electrical stimulation were displayed continuously on multichannel neurophysiologic equipment. The careful titration of the electrical stimulation delivered through the UA while tapering the current intensity with the progression of the resection was used as the main strategy. Results All operations were performed successfully, and facial nerve conduction was maintained in all patients except one, in whom a permanent lesion of the facial nerve followed a miscommunication to the neurosurgeon. Conclusion The coupling of the electrical stimulation to the UA provided the neurosurgeon with an efficient and cost-effective tool and allowed a safe resection. Positive responses were obtained from the facial muscles with low current intensity (lowest intensity: 0.1 mA). The availability of a resection tool paired with a stimulator allowed the surgeon to improve the surgical workflow because fewer interruptions were necessary to stimulate the facial nerve via a handheld probe.

scholarly journals Some open mapping theorems for measures

1972 ◽  
Vol 164 ◽  
pp. 287-287 ◽  
Author(s):  
Seymour Ditor ◽  
Larry Q. Eifler
Keyword(s):  
Open Mapping

scholarly journals A note on the idempotent measures on countable semigroups

1970 ◽  
Vol 11 (4) ◽  
pp. 417-420
Author(s):  
Tze-Chien Sun ◽  
N. A. Tserpes
Keyword(s):  
Probability Measure ◽  
Continuous Mapping ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Left Zero ◽  
Product Topology ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Image Position ◽  
Completely Simple

In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then(a) F is a closed completely simple subsemigroup.(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

A note on semi-open and almost open induced maps

2021 ◽  
pp. 107823
Author(s):  
Alvaro Andrade ◽  
Javier Camargo
Keyword(s):  
Almost Open ◽  
Induced Maps
Sign in / Sign up

Export Citation Format

Share Document